April 5 (Reuters) - U.S. energy firms this week cut the number of oil and natural gas rigs operating for a third week in a row for the first time since October, 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, fell by one to 620 in the week to April 5, the lowest since early February.

Baker Hughes said that puts the total rig count down 131, or 17%, below this time last year.

Baker Hughes said oil rigs rose two to 508 this week, while gas rigs fell by two to 110, their lowest since January 2022.

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 22% so far in 2024 after dropping by 11% in 2023. U.S. gas futures, meanwhile, were down about 28% so far in 2024 after plunging by 44% in 2023.

That increase in oil prices should encourage drillers to boost U.S. crude output from a record 12.9 million barrels per day (bpd) in 2023 to 13.2 million bpd in 2024 and 13.6 million bpd in 2025, according to the latest U.S. Energy Information Administration (EIA) outlook.

But the drop in gas prices to a 3-1/2-year low in February and March will cut U.S. gas output to 103.4 billion cubic feet per day (bcfd) in 2024 from a record 103.8 bcfd in 2023, according to the EIA, as some producers slash spending and reduce drilling activities.

Analysts, however, said it could take a few months for those planned gas rig reductions to show up in the data. (Reporting by Scott DiSavino Editing by Marguerita Choy)