Jan 13 (Reuters) - U.S. energy firms this week added oil and natural gas rigs for the first time in three weeks, energy services firm Baker Hughes Co said in its closely followed report on Friday.

The oil and gas rig count, an early indicator of future output, rose three to 775 in the week to Jan. 13.

Baker Hughes said that puts the total rig count up 174, or 29%, over this time last year.

U.S. oil rigs rose five to 623 this week, in their biggest build since November, while gas rigs fell two to 150, their lowest since May.

U.S. oil futures were down about 1% so far this year after gaining about 7% in 2022.

The U.S. Energy Information Administration this week raised its forecast for crude output growth.

U.S. crude production was on track to rise from 11.9 million barrels per day (bpd) in 2022 to 12.4 million bpd in 2023 and 12.8 million bpd in 2024, according to the EIA. That compares with a record 12.3 million bpd in 2019.

However, shale producer EOG Resources Inc last week said it anticipates its activity in the Permian Basin, the largest U.S. oilfield, to be flat this year, as supplies and equipment remain expensive and as it focuses on shareholder returns. (Reporting by Scott DiSavino Editing by Marguerita Choy)