Futures had fallen earlier in the session on news that a container ship in the Suez Canal blocking traffic for nearly a week had been refloated.
Brent oil rose 26 cents to $64.83 a barrel by 1:08 p.m. EDT (1708 GMT). U.S. crude rose 47 cents to $61.44 a barrel.
Russia will support broadly stable oil output by the Organization of the Petroleum Exporting Countries and allies including Russia (OPEC+) in May, while seeking a relatively small output hike for itself to meet the rising seasonal demand, according to a source familiar with Russia's thinking.
Sources told Reuters last week that they expect a decision similar to the last meeting when OPEC+ meets on April 1 to decide output policy.
Russian oil and gas condensate output increased to 10.22 million barrels per day (bpd) in the period March 1-28 from 10.1 million bpd in February, two industry sources familiar with the data told Reuters, broadly in line with Moscow's plans.
At the Suez Canal, live footage on a local television station showed the ship Ever Given surrounded by tug boats moving slowly in the centre of the canal on Monday. The station, ExtraNews, said the ship was moving at a speed of 1.5 knots.
However, disruptions in the global shipping industry could take weeks and possibly months to clear, top container shipping lines said.
"The market will soon realize that despite the positive news, even if Ever Given leaves the Canal within days, some leftover downstream ripple effects should be expected in the meantime," said Louise Dickson, oil markets analyst.
Limiting price gains, some European countries struggling with increased COVID-19 infections have tightened lockdown restrictions, and fuel demand across the continent remains weak. England's stay-at-home lockdown order, though, ended on Monday.
(Reporting by Stephanie Kelly in New York; additional reporting by Bozorgmehr Sharafedin in London and Aaron Sheldrick in Tokyo, Editing by Marguerita Choy and Gareth Jones)
By Stephanie Kelly
