November U.S. West Texas Intermediate (WTI) crude futures settled at $41.46 a barrel, up 63 cents, or 1.54%. The more active December contract settled at $41.70, gaining 64 cents.

Brent crude futures for December delivery settled at $43.16 a barrel, rising 54 cents, or 1.27%.

Investors are following negotiations between U.S. House of Representatives Speaker Nancy Pelosi and Treasury Secretary Steven Mnuchin over another U.S. coronavirus aid package, said John Kilduff, partner at Again Capital in New York.

"If we get a deal, I think that would be supportive, and if we don't get a deal, I think that's going to be somewhat punishing for prices," Kilduff said.

Prices picked up after Pelosi said she was optimistic Democrats could reach an agreement with the White House that could get aid out by early next month. She added there should be an indication of a possible agreement later on Tuesday.

Still, skepticism over the impact of a deal on oil markets lingered.

"Even allowing for a fresh stimulus package, risk appetite could take a hit from an unfolding of the 'buy the rumor/sell the news' phenomena,'" said Jim Ritterbusch of Ritterbusch and Associates. "With this possibility in mind, we will be looking to short December crude at or above the $42 mark for a trading turn to the downside."

The rebound in COVID-19 cases in Europe and North America that has sparked renewed lockdown measures kept prices from moving higher.

A ministerial panel of the Organization of the Petroleum Exporting Countries (OPEC) and its allies, together known as OPEC+, pledged on Monday to support the market in the face of the pandemic's hit to demand.

However, those countries plan on scaling back the size of its production cuts in January from a current 7.7 million barrels per day (bpd) to roughly 5.7 million bpd in January.

OPEC member Libya, which is exempt from the cuts, is also ramping up production after armed conflict shut almost all of the country's output in January, pumping more oil into an oversupplied market.

Adding to supply worries, crude inventories rose by 584,000 barrels in the week to Oct. 16 to about 490.6 million barrels, data from industry group the American Petroleum Institute showed, compared with analysts' expectations in a Reuters poll for a draw of 1 million barrels.

(Additonal reporting by Ahmad Ghaddar in London, Sonali Paul in Melbourne and Roslan Khasawneh in Singapore; Editing by Marguerita Choy, Jason Neely and Jonathan Oatis)

By Laila Kearney