Brent crude futures were up nearly 1.4pc, or 50 cents to $36.03 a barrel as of 0840 GMT.
US West Texas Interme
Brent crude futures were up nearly 1.4pc, or 50 cents to $36.03 a barrel as of 0840 GMT.
US West Texas Intermediate (WTI) crude futures was up 2.6pc, or 86 cents, at $34.11 a barrel.
There was no WTI settlement on Monday because of the US Memorial Day holiday.
The market was buoyed by comments from Russia that its oil output had dropped almost to its target of 8.5 million barrels per day (bpd) for May and June under the supply cut deal agreed by major producers (OPEC+).
OPEC+ countries are set to meet again in early June to discuss maintaining their supply cuts to shore up prices, which are still down about 45pc since the start of the year.
The world's major producers, including Saudi Arabia and Russia, agreed in April to cut their collective output by nearly 10 million bpd for May and June.
Russia's energy ministry on Monday quoted minister Alexander Novak as saying a rise in fuel demand should help cut a global surplus of about 7 million to 12 million bpd by June or July.
"Russia is clearly committed to continued cuts also in H2-20 so the upcoming OPEC+ meeting on the 9th of June is unlikely to be a bearish surprise like the one that fell apart on the 6th of March," SEB chief commodities strategist Bjarne Schieldrop said.
Data from energy services firm Baker Hughes, meanwhile, showed the US rig count hit a record low of 318 in the week to May 22, also indicating lower output in the future.