May 17 (Reuters) - U.S. energy firms this week added oil and natural gas rigs for the first time in four weeks, energy services firm Baker Hughes said in its closely followed report on Friday.

The oil and gas rig count, an early indicator of future output, rose by one to 604 in the week to May 17.

Despite this week's rig increase, Baker Hughes said the total count was still down 116, or 16% below this time last year.

Baker Hughes said oil rigs rose by one to 497 this week, while gas rigs were unchanged at 103.

The oil and gas rig count dropped about 20% in 2023 after rising by 33% in 2022 and 67% in 2021, due to a decline in oil and gas prices, higher labor and equipment costs from soaring inflation and as companies focused on paying down debt and boosting shareholder returns instead of raising output.

U.S. oil futures were up about 11% so far in 2024 after dropping by 11% in 2023. U.S. gas futures were up about 3% so far in 2024 after plunging by 44% in 2023.

Oil output from

top shale-producing regions

will rise in June to its highest in six months, while gas production in the big shale basins will slide to a five-month low, the U.S. Energy Information Administration (EIA) said in its monthly Drilling Productivity Report on Monday.

Shale production, which represents about three-quarters of total U.S. oil output, is rising due to improved well productivity. Production per new rig in the Permian basin that straddles West Texas and New Mexico, is expected in June to reach the highest monthly output per rig since November 2021. (Reporting by Scott DiSavino Editing by Marguerita Choy)