Brent crude was up 38 cents, or 0.6%, at $61.52 a barrel by 11:06 a.m. ET (1606 GMT) having dropped to a session low of $60.35 earlier. U.S. oil was up 22 cents, or 0.4%, at $58.46 after falling to a session low of $57.41.

U.S. crude was on track for a weekly gain of about 2.8% while Brent was set for a 3.6% rise on the week.

U.S. President Joe Biden will meet with a bipartisan group of mayors and governors as he keeps pushing for approval of a $1.9 trillion coronavirus relief plan to bolster economic growth and help millions of unemployed workers.

All three major U.S. stock indexes were on course for their second straight weekly rise. A sharp drop in new COVID-19 cases and hospitalizations buoyed hopes life will eventually return to normal.

"Expected U.S. stimulus and ongoing vaccine progress is likely to maintain appetite for risky assets in offering support to the oil market," said Jim Ritterbusch, president of Ritterbusch and Associates in Galena, Illinois.

Oil prices have risen over recent weeks partly owing to production cuts from the Organization of the Petroleum Exporting Countries (OPEC) and allied producers in the group OPEC+.

This week, OPEC ratcheted down expectations for global oil demand to recover in 2021, trimming its forecast by 110,000 barrels per day (bpd) to 5.79 million bpd.

The International Energy Agency (IEA) said oil supply was still outstripping global demand, though COVID-19 vaccines are expected to support a demand recovery.

"The (IEA) report paints a more pessimistic picture than market participants have presumably been envisaging given the current high prices," Commerzbank said.

Demand data from the world's biggest oil importer also paints a bleak picture.

The number of people who travelled in China ahead of Lunar New Year holidays plummeted by 70% from two years ago as coronavirus restrictions curbed the world's largest annual domestic migration, official data showed.

ABN Amro revised its 2021 Brent oil prices forecast slightly higher to $55 a barrel but warned of demand headwinds.

"The biggest recovery in demand will have to come from the aviation sector," the bank said. "Especially for aviation, we do not yet see a major recovery this year."

(Additional reporting by Ahmad Ghaddar in London, Aaron Sheldrick in Tokyo; Editing by David Goodman, Jan Harvey and David Gregorio)

By Devika Krishna Kumar