Brent futures were up 66 cents, or 1%, at $64.86 a barrel by 12:45 p.m. EST (1745 GMT), while US West Texas Intermediate (WTI) crude was up 39 cents, or 0.7%, at $58.47.
That put WTI front-month futures on track to close below the second month for the first time since Nov. 19, which is known in the trading industry as contango.
In addition, oil also found technical support after WTI fell to a more than five-week low of $57.72 before bouncing off the 200-day moving average.
The outlook for oil demand was supported by the expected signing of a Phase 1 US-China trade agreement on Wednesday, marking a major step in ending a dispute that has cut global growth and dented demand for oil.
"Oil prices are tentatively rebounding after seller exhaustion kicked (in) as investors await the next developments on the trade front and whether we see a strong pickup with global demand following the phase-one trade deal," Edward Moya, senior market analyst at OANDA in New York, said in a report.
China has pledged to buy more than $50 billion in energy supplies from the United States over the next two years, according to a source briefed on the trade deal.
Despite the trade dispute, China's crude oil imports in 2019 surged 9.5% from the previous year, setting a record for a 17th straight year as demand growth from new refineries propelled purchases by the world's top importer, data showed.
However, gains were limited as concerns about possible supply disruptions eased due to a decline in tensions in the Middle East.
The recent declines came as investors unwound bullish positions built after the recent killing of a senior Iranian general in a US air strike which sent oil prices to a four-month high earlier this month, said Harry Tchilinguirian, global oil strategist at BNP Paribas in London.
"As geopolitical tensions take a back seat for now, we may see more of the same in the short term," Tchilinguirian told the Reuters Global Oil Forum.
Saudi Arabia's energy minister, Prince Abdulaziz bin Salman, said his country would work for oil market stability amid heightened US-Iranian tensions.
He also said it was too early to talk about whether the Organization of the Petroleum Exporting Countries (OPEC) and its allies, a group known as OPEC+, would continue with production curbs that are due to expire in March.
Separately, US crude oil inventories likely declined by 0.8 million barrels last week, a preliminary Reuters poll showed on Monday.
The poll was conducted ahead of reports from the American Petroleum Institute (API), an industry group, on Tuesday, and the Energy Information Administration on Wednesday.