Dec 1 (Reuters) - U.S. energy firms this week added oil and natural gas rigs for a third week in a row, 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 three to 625 in the week to Dec. 1.

Despite this week's rig increase, Baker Hughes said the total count was still down 159, or 20%, below this time last year.

U.S. oil rigs rose five to 505 this week, their highest since September, while gas rigs fell by one to 116.

The combined rig count has dropped from the post-pandemic high of 784 a year ago due to lower oil and gas prices. Capital spending has also gone to cover inflation-related costs for labor and equipment as many firms focus on returning money to investors and paying down debt rather than boosting oil and gas production.

U.S. oil futures were down about 6% so far this year after gaining 7% in 2022. U.S. gas futures, meanwhile, have plunged about 37% so far this year after rising about 20% last year.

U.S. crude production, however, rose to a new monthly record of 13.2 million barrels per day in September, while natural gas output also remained near its record high, Energy Information Administration data showed this week.

Oil and gas output was still on track to hit record highs in 2023 and 2024 as firms complete work on their already drilled wells. (Reporting by Scott DiSavino Editing by Marguerita Choy)