Dec 3 (Reuters) - U.S. energy firms this week maintained the number of oil and natural gas rigs with oil prices on track to fall for a sixth week in a row.

The U.S. oil and gas rig count, an early indicator of future output, held at 569 in the week to Dec. 3, keeping at its highest since April 2020, energy services firm Baker Hughes Co said in its closely followed report on Friday.

That puts the total rig count up 246 rigs, or 76%, over this time last year.

U.S. oil rigs held at 467 this week, which was also their highest since April 2020, while gas rigs were unchanged at 102 for a fourth week in a row.

U.S. crude futures were trading around $67 per barrel on Friday, putting the contract on track to decline for a sixth week in a row for the first time since November 2018.

But with oil prices still up about 38% this year, some energy firms plan to raise spending, after cutting drilling and completion expenditures in 2019 and 2020, while others focus on shareholder returns over increasing production.

Chesapeake Energy Corp, once the second-largest U.S. natural gas producer, this week continued to double down on its return of capital commitment, becoming the latest shale producer to focus on shareholder management.

The top two U.S. oil producers are among the other companies that have resumed share repurchases after halting them last year, while releasing positive spending plans this week.

Exxon Mobil Corp extended its previously projected investment rate for two years, with the Permian, the top U.S. oilfield, one of its top oil project priorities, while Chevron Corp plans to boost spending on new oil and gas projects in 2022 by 20%.

U.S. financial services firm Cowen & Co said the independent exploration and production (E&P) companies it tracks plan to increase spending about 4% in 2021 versus 2020, and 12% in 2022 versus 2021 for the dozen or so firms that have already announced estimates for next year.

That follows capital expenditure reductions of roughly 48% in 2020 and 12% in 2019. (Reporting by Scott DiSavino Editing by Marguerita Choy)