NEW YORK, June 5 (Reuters) - The dollar index turned negative on Monday after data showed that the U.S. services sector barely grew in May as new orders slowed, overturning an earlier rally that was boosted by strong jobs growth in May.

The Institute for Supply Management (ISM) said that its non-manufacturing PMI fell to 50.3 last month from 51.9 in April. A reading above 50 indicates growth in the services industry, which accounts for more than two-thirds of the economy.

Economists polled by Reuters had forecast the non-manufacturing PMI edging up to 52.2.

The dollar index fell to 103.96, down 0.18% on the day, after earlier climbing as high as 104.40. It is holding just below a 11-week high of 104.70 reached on May 31.

The euro was last up 0.10% at $1.0718, just above the low of $1.0635 from May 31, which was the lowest since March 20.

The greenback fell 0.51% to 139.28 yen . It reached 140.93 on May 30, the highest since Nov. 23.

The dollar had risen earlier on Monday on follow through from Friday's better than expected jobs gains for May, which added to expectations the Federal Reserve may continue hiking rates as inflation remains elevated.

U.S. job growth accelerated by 339,000 jobs in May, but a surge in the unemployment rate to a seven-month high of 3.7% suggested that labor market conditions were easing.

“Job gains continue to surprise meaningfully to the top side, the labor market continues to be very strong,” said Brian Daingerfield, head of G10 FX strategy at NatWest Markets in Stamford, Connecticut.

The U.S. central bank is viewed as most likely to leave rates unchanged in June, but fed funds futures traders are pricing in a 67% likelihood of at least an additional 25 basis points rate hike by July, according to the CME Group’s FedWatch tool.

Fed officials including vice chair nominee Philip Jefferson have stressed that any decision by the Fed to hold its benchmark overnight interest rate steady at an upcoming meeting should not be taken to mean the U.S. central bank is done tightening monetary policy.

“You could think of a skip as maybe part of the slowing of the tightening cycle rather than a pause in the tightening cycle,” said Daingerfield.

Fed officials are now in a blackout period before the June 13-14 meeting.

Euro zone data on Monday showed that business growth slowed in May, though the bloc's dominant services industry offset a deepening decline in the manufacturing sector.

European Central Bank President Christine Lagarde on Monday acknowledged "signs of moderation" in core inflation in the euro zone but reaffirmed it was too early to call a peak in that key gauge of price growth.

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Currency bid prices at 10:27AM (1427 GMT)

Additional reporting by Iain Withers in London; Editing by Kirsten Donovan

Our Standards: The Thomson Reuters Trust Principles.

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