While that remains about twice the rate that was normal before the onset of the coronavirus pandemic in 2020, it is down sharply from a peak of about 9 percent last summer.

The fresh data offer the latest evidence that the Fed’s push to control rapid price increases is beginning to work. Fed officials have been raising interest rates since March 2022 to make it more expensive to borrow money, in a bid to slow consumer demand, tamp down a strong labor market and ultimately cool rapid inflation. They have lifted borrowing costs for 10 meetings in a row, to just above 5 percent, and many officials have suggested in recent weeks that they could soon take a pause to give themselves more time to assess how those adjustments are working.

Investors have been betting that Fed officials will leave rates unchanged at their meeting this week, breaking their long streak of increases. But they had also penciled in a small chance that policymakers might lift rates — a possibility that all but disappeared after Tuesday’s inflation figures. Even so, many investors continue to expect that Fed officials will restart rate increases in July.

“They are probably feeling a little bit relieved,” Laura Rosner-Warburton, a senior economist at MacroPolicy Perspectives, said. The report included both encouraging and discouraging news for policymakers, she said: “It lets them pause, but it keeps them pretty firmly on track” to raise rates again in the future.

Taken as a whole, the data suggested that while the inflation that has been plaguing consumers and bedeviling the Fed for two years remains stubborn, it is also meaningfully slowing. A cooling economy and a gradually weakening job market could help to further weigh down inflation in the months to come, which would give central bankers confidence that they have lifted borrowing costs enough to bring prices back under control.

The report showed that a closely watched inflation measure that strips out food and fuel prices to give a sense of underlying trends continued to slow in May on an annual basis. That “core” price index rose 5.3 percent in May compared with a year earlier. That was above the 5.2 percent economists had expected, but down from 5.5 percent the previous month.

That cooling comes as costs for some key services climb more slowly or even decline. Rental inflation has long been expected to cool off, and that is beginning to happen. Airfares came down sharply last month, and a range of recreation-related purchases — from movie tickets to pet care — moderated in price.

Fed officials try to keep inflation at 2 percent on average over time, using a different but related measure — the Personal Consumption Expenditures index. The Consumer Price Index measure comes out a few weeks earlier and contains data that feeds into the Fed’s preferred measure, which is why investors watch it so closely for a signal of where inflation is heading.

The central bank’s two-day meeting starts Tuesday and will conclude Wednesday afternoon, when officials are scheduled to release their interest rate decision. That announcement will be accompanied by a fresh set of economic projections — the first ones central bankers have released since March. Jerome H. Powell, the Fed chair, is scheduled to give a news conference to explain both the decision and the outlook.

Officials are trying to strike a delicate balance: They want to slow the economy enough to make sure that inflation is fully stamped out, but without hitting the brakes so hard that growth grinds to a halt and workers unnecessarily lose jobs.

Prices for groceries rose 0.1 percent in May, up from April, when prices declined 0.2 percent. Prices for food at restaurants continued to climb, rising 0.5 percent over the month, an increase from 0.4 percent in April.

Food prices are rising at a slightly slower rate than they were a few months ago, but they are still much higher than they were before the pandemic. Food prices have picked up 6.7 percent over the last year.

Fruit and vegetable prices increased 1.3 percent in May, following a 0.5 percent decrease in April. The index for meats, poultry, fish and eggs fell 1.2 percent in May after declining 0.3 percent in April.

The price of eggs fell 13.8 percent, the largest decrease in that index since January 1951. That came after egg prices declined 1.5 percent in April and 10.9 percent in March. Egg prices had jumped a few months ago after an outbreak of bird flu and the cost of fuel, feed and packaging rose.

Food prices began rising sharply about two years ago as the costs of labor, transportation and raw materials increased, partly because of supply chain snarls and higher fuel prices. That resulted in companies passing along some cost increases to consumers. Other factors, such as extreme droughts in the Western United States, have also strained supply and pushed up food prices.

Though costs for some food ingredients and other raw materials have fallen in recent months, some large corporations, such as PepsiCo, have signaled that they will continue increasing prices or keep them elevated for the foreseeable future as consumers have largely kept buying products.

Still, economists say that overall food prices could show signs of moderating as labor pressures ease and wage growth across the food industry has slowed, reducing stress for companies. Recent declines in fuel prices have also helped bring down transportation costs.

Biden administration officials have highlighted the recent slowdown in price increases for groceries, although they have said, “The job is not done yet and there is considerable uncertainty around the outlook.”

Some shoppers have started to notice some relief at the grocery store, but they have continued to grumble over the steep cost of food.

Hanna Hensley, 29, an assistant high school teacher who was shopping at a Giant Food store in Arlington, Va., on Sunday, said she was frustrated with the high cost of food, which has become more of a strain on her budget. She said weekly groceries for her family, which includes her parents and sister, now total about $100, up from about $70 before the pandemic.

She said she was glad, though, to see prices for some items come down. When egg prices shot up to around $5 a carton a few months ago, she stopped buying them. But she said a dozen eggs now cost her about $2.50, and on Sunday, she picked up a carton of them, along with oatmeal, tomatoes, mushrooms and sliced marble cake.

Ms. Hensley said she had noticed that overall food costs were not rising as much as they had been a few months ago, and she hoped prices would fall or at least remain stable.

“Budgeting is hard when prices are constantly changing,” she said.

The Consumer Price Index for May was initially read by investors as moderate enough to ensure the Federal Reserve will hold off on another interest rate increase this week. The central bank will announce its decision on Wednesday.

The S&P 500-stock index rose 0.7 percent on Tuesday, to its highest level since January of 2022, extending a strong rally since the index fell to a low point in October. The S&P 500 has climbed more than 20 percent from that 2022 low, a gain that by one definition breaches the threshold for a bull market, a marker of a new phase of exuberance in the markets.

Slowing inflation is seen by investors and economists as limiting the need for the Federal Reserve to keep increasing interest rates, with increases so far having raised borrowing costs for consumers and companies and weighed on the broader stock market. Some policymakers had already suggested the Fed might not raise rates again this month, and after the latest inflation data, the likelihood of an increase was close to wiped out in markets.

Not all investors agree on the best way to define a bull market, especially when concerns over the longer-term trajectory of the U.S. economy remain. The S&P 500 is still roughly 9 percent off its record high, reached at the start of 2022, just before fears of rising interest rates in response to accelerating inflation set in and dragged the index to a loss of around 20 percent.

“With inflation stubbornly high, we do see the business cycle eventually ending in recession,” noted Alexandra Wilson-Elizondo, deputy chief investment officer of multi-asset solutions at Goldman Sachs Asset Management.

Investor exuberance is nonetheless spreading. The Russell 2000 index, which tracks smaller companies in the United States that are more exposed to the domestic economy, has rallied more than 8 percent this month, and jumped more than 1 percent in response to the inflation report.

The index had trended sideways for much of the year, and even after its rally, it remains less than 15 percent above a low reached 12 months ago.

However, the Russell 2000’s recent rise is still indicative of the rally taking hold across the stock market as inflation cools and the economy has remained resilient to the potentially damaging effects higher interest rates can bring.

“We are just over two weeks away from the beginning of the third quarter. This is meaningful because to start the year there was a near consensus view that this is when the recession would begin,” said Ms. Wilson-Elizondo. “Today, the recession has not arrived.”

The S&P 500 rose 0.6 percent as stock markets opened for the day, with investors seeing the fresh inflation data as staying the Fed’s hand on rate increases.

The data was “not a strong enough read to warrant the Fed deviating from its telegraphed intention" to keep rates steady at tomorrow's meeting, noted analysts at BMO Capital Markets.

President Biden credited his domestic agenda for lowering inflation in an optimistic written statement. “After gas and grocery prices increased rapidly last year due to the war in Ukraine, inflation has fallen for 11 months in a row,” Biden said. “While there is more work to do, the plan that I laid out a year ago to bring down the cost of living and sustain stable and steady growth is working.”

It’s always worth pointing out what we mean when we say “inflation has fallen” — wording that can cause some confusion. It does not mean that prices are falling. Instead, it means that prices are still increasing when compared to the previous year’s price level, but they are increasing more slowly than they had in the previous month.

Economists have been expecting a slowdown. For months now, private-sector rent trackers from sites like Zillow and Apartment List have been showing rents rising more slowly, or falling outright in some cities. Those sources react more quickly to changes in the rental market, partly because they are based only on new leases, unlike the government’s measure, which tries to capture rent paid by both new and existing tenants. Over time, however, the different measures should converge.

Forecasters expect the Labor Department’s measure of rents to continue to ease over the next few months. That’s good news for the Federal Reserve because rent — along with other housing costs, which are closely related — is by far the largest component of the Consumer Price Index.

Still, housing costs are what economists call “sticky”: they tend to move only gradually. That means that while rents may have begun to ease, it is unlikely they will fall rapidly, which could keep overall inflation uncomfortably high in coming months.

The car market was one of the earliest instigators of more widespread inflation in 2021, as factory stoppages and semiconductor shortages collided with a wave of buyers moving to more remote areas and going on road trips with full wallets.

To preserve their profit margins, automakers used sparse supplies for higher-value vehicles like trucks and sport utility vehicles. They’ve stuck to that strategy, while introducing electric vehicles and dropping cheaper models, keeping price growth higher than it might have been otherwise.

Wholesale prices for used vehicles have been coming down in recent months, according to Cox Automotive’s Manheim used vehicle price index, indicating that cars may become more affordable this summer.

Other expenses associated with car ownership have continued to grow rapidly above prepandemic levels: maintenance and repair is up 25 percent, for example, and insurance has climbed 21 percent. Car and truck rental, while easing off its price highs, is 26 percent above its level in February 2020.

Investors moved swiftly to price out almost any possibility that the Federal Reserve raises interest rates tomorrow, following the fresh inflation data that met economists' expectations.

Futures for the S&P 500 nudged 0.3 percent higher on Tuesday morning, extending a rise on Monday. The benchmark stock index has recorded four straight weeks of gains.

Investors have become more optimistic about today's inflation report, which is expected to show a moderating pace of rising prices that market watchers think is unlikely to alter the Fed's holding interest rates steady at its meeting tomorrow.

The U.S. West Texas Intermediate benchmark price is even lower, and oil is now selling for roughly half as much as it was last summer. That has helped drive down prices for gasoline, diesel and other fuels. American drivers paid an average of $3.59 for regular gasoline on Monday, compared with $5.01 a year ago, according to the AAA motor club. The price of diesel, the fuel used in trucks and other heavy transportation, has dropped even more drastically.

The weakness in oil and fuel prices could, over time, help bring down broader inflation because energy prices played a big role last year in making many goods and services more expensive.

Oil prices have been falling in part because countries like Guyana, Brazil, Iran and Russia are increasing production and sales. Despite Western sanctions and an OPEC Plus agreement in the spring to cut production, Russia has been exporting more oil to China and India at steep discounts.

Perhaps an even bigger reason oil prices are falling is that the Chinese economy has not taken off after officials there loosened pandemic policies. Many commodity traders fear that global demand for oil and other fuels could weaken further later this year as industrial activity slows around the world.

“Demand is looking weaker and non-OPEC supply stronger by year-end,” analysts at Citi Investment said in a research note this week.

But many of those price categories are now cooling. Hotel prices have recently climbed much more slowly on a year-over-year basis, and airfares fell in May, a report on Tuesday showed. If that trend continues this summer, it could contribute to a continuing slowdown in overall services inflation, something the Fed has been watching and waiting for.

“We see some slowing in so-called revenge categories,” said Yelena Shulyatyeva, senior U.S. economist at BNP Paribas, said ahead of the fresh inflation data.

Omair Sharif, founder of the firm Inflation Insights, said ahead of the report that he expects airfares and hotel costs to weigh on inflation in June and July. He does not expect hotels and domestic air travel to see the same sort of surge this summer that they experienced last year.

“We’re just not getting the same kind of pop any longer,” he said. “Airfares have pretty much stalled out.”

Consumers are not only getting back to more normal living patterns, they may also be increasingly cautious as they face high costs after several years of rapid inflation — and as they worry that the Fed’s interest rate increases might soon push the economy into a recession.