Dec 9 (Reuters) - U.S. energy firms this week cut the number of oil and natural gas rigs operating for the first time in six weeks as oil prices fell to their lowest this year.

The U.S. oil and gas rig count, an early indicator of future output, fell by four to 780 in the week to Dec. 9, energy services firm Baker Hughes Co said in its closely followed report on Friday. <RIG-USA-BHI> <RIG-OL-USA-BHI> <RIG-GS-USA-BHI>

U.S. oil rigs fell two to 625 this week, while gas rigs declined by two to 153, their lowest since July.

U.S. oil futures were trading around $71 a barrel on Friday, down about 6% so far this year, after topping $130 in March after Russia's invasion of Ukraine.

The two largest U.S. oil companies - Exxon Mobil Corp and Chevron Corp - this week disclosed plans to increase outlays on energy projects next year amid high oil demand and prices.

While spending more, it will be less than half the combined $84 billion they spent in 2013, when oil prices often traded above $100 per barrel as it has this year. The two are awash in cash from those prices and past cost-cuts, and have sharply raised shareholder payouts, rather than boosting output.

U.S. crude production was on track to rise from 11.25 million barrels per day (bpd) in 2021 to 11.87 million bpd in 2022 and 12.34 million bpd in 2023, according to federal energy data. That compares with a record 12.32 million bpd in 2019.

U.S. financial services firm Cowen & Co has said the independent exploration and production (E&P) companies it tracks plan to boost spending by about 40% in 2022 versus 2021 after increasing spending about 4% in 2021 versus 2020.

That follows a drop in capital expenditures of roughly 48% in 2020 and 12% in 2019.

Some analysts, however, have noted that even when energy firms do boost their capital expenditures, it was not necessarily to increase production but was instead being spent on more expensive pipes and other equipment and rising labor costs due to soaring inflation and supply disruptions. (Reporting by Scott DiSavino Editing by Marguerita Choy)