By Jessica Resnick-Ault

NEW YORK (Reuters) -Oil prices rose 2% on Tuesday, reaching their highest in 12 months after major producers showed they were reining in output roughly in line with their commitments.

The global and U.S. crude benchmarks rallied as optimism about more U.S. economic stimulus added to market bullishness from OPEC production levels, which rose less than expected in January.

Brent crude settled up $1.11, or 2%, at $57.46 a barrel, after its third straight day of gains. During the session, it touched $58.05, the highest levels since January last year.

U.S. oil gained $1.21, or 2.3%, to close at $54.76, after hitting a session high of $55.26, the highest in a year.

Crude output from the Organization of the Petroleum Exporting Countries rose in January for a seventh month but the increase was smaller than expected, a Reuters survey found.

Voluntary cuts of 1 million barrels per day by OPEC’s de facto leader, Saudi Arabia, are set to be implemented from the beginning of February through March.

Russian output increased in January but is in line with the OPEC+ supply pact, while in Kazakhstan, oil volumes fell for the month.

The rally picked up steam as the U.S. Congress looked ready to adopt an economic stimulus package, and as cold U.S. weather boosted heating oil demand.

“You got the U.S. economic stimulus package that no one thought we would get,” said Bob Yawger, director of energy futures at Mizuho in New York.

The Democratic-led U.S. House of Representatives prepared to take the first step forward on President Joe Biden’s $1.9 trillion COVID-19 relief package on Tuesday, with a key vote expected to fast-track the measure through Congress.

A cold snap and heavy snow in the U.S. Northeast drove the margin for heating oil to an 8-month high of $15.84, lending further support to crude.

U.S. distillate fuel stockpiles, including heating oil, were forecast to have dropped 400,000 barrels last week, according to a Reuters poll. Crude stockpiles were expected to rise by 400,000 barrels. [EIA/S]

Inventory estimates from the American Petroleum Institute, a trade group, are expected at 4:30 p.m. (2130 GMT), and government figures follow on Wednesday. [API/S]

However, energy giant BP flagged a difficult start to 2021 amid declining product demand, noting that January retail volumes were down about 20% year-on-year, compared with a decline of 11% in the fourth quarter.

Oil demand is nevertheless expected to recover in 2021, BP said, with global inventories seen returning to their five-year average by the middle of the year.

(Additional reporting by Noah Browning and Aaron SheldrickEditing by Marguerita Choy and David Gregorio)