May 19 (Reuters) - U.S. energy firms this week cut 11 oil rigs, the most in a week since September 2021, energy services firm Baker Hughes Co (BKR.O) said in its closely followed report on Friday.

That follows last week's cut of 17 natural gas rigs, which was the biggest drop since June 2020.

The oil and gas rig count, an early indicator of future output, fell by 11 to 720 in the week to May 19, the lowest since May 2022. , ,

Baker Hughes said that puts the total rig count down eight, or 1%, below this time last year, the first time since April 2021 that rigs were lower than the year-ago level.

U.S. oil rigs fell by 11 to 575 this week, their lowest since June 2022, while gas rigs were unchanged at 141.

Most of the rig reductions were in Texas where the total count dropped by nine to 355 this week, the lowest since May 2022.

Texas lost three rigs in the Eagle Ford shale, bringing the total in that basin down to 59, the lowest since April 2022. The state also lost four rigs in the Permian, bringing the total in that basin down 349, the lowest since March.

In New Mexico, meanwhile, the count rose by one to 109, its highest since February.

New Mexico's oil production grew more last year than any other state, including top producer Texas, and accounted for half the nation's overall gain, signaling its importance in expanding U.S. oil output.

Data provider Enverus, which publishes its own rig count data, said drillers cut six rigs in the week to May 17, dropping the overall count to 780. That put the count down about 35 rigs over the past month and down 5% over the past year.

U.S. oil futures were 11% so far this year after gaining about 7% in 2022. U.S. gas futures , meanwhile, have plunged about 42% so far this year after rising about 20% last year.

The drop in prices has already caused some exploration and production companies to cut rigs, especially gas rigs, with many still focusing more on returning money to investors and paying down debt rather than boosting output.

Despite some plans to lower rig counts, U.S. oil output from the seven biggest shale basins is due to rise in June to the highest on record, according to the Energy Information Administration's projections this week.

Reporting by Scott DiSavino Editing by Marguerita Choy

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Covers the North American power and natural gas markets.

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