Light sweet crude for February delivery rose 49 cents to $62.90 a barrel in electronic trading.
Brent crude traded up 63 cents to $63.05 a barrel on London's ICE Futures exchange, which reopened Tuesday after a three-day closure for the Christmas weekend.
Before the holiday, prices slipped as brokers weighed slower economic growth and expectations of a mild winter _ which would slow demand for heating oil _ against OPEC's determination to tighten up worldwide supplies.
The Organization of Petroleum Exporting Countries said earlier this month that it plans to reduce output by an additional 500,000 barrels a day beginning in February. That comes on top of a previously announced cut of 1.2 million barrels per day.
The market was also watching geopolitical developments in Iran, where the government was expected to decide Tuesday whether it would stop cooperating with the International Atomic Energy Association. Iran has defiantly vowed to continue uranium enrichment despite U.N. economic sanctions passed Saturday aimed at forcing a rollback in its nuclear program.
Nuclear negotiator Ali Larijani was quoted as saying that Iran would begin work at the Natanz nuclear plant on Sunday in response to the sanctions.
Oil-rich Iran insists its nuclear program is intended only to produce fuel for nuclear reactors that would generate electricity, but Washington and some allies suspect its ultimate goal is to create atomic weapons in violation of Iran's treaty commitments.
"Don't look for a major washout in prices anytime soon. ... Trouble in the world's most important oil-producing region is not going away," analysts at Fimat USA said in their daily note to clients.
In other Nymex trading Tuesday, heating oil futures rose 1.72 cents to $1.7385 a gallon, while natural gas prices dropped 24.5 cents to $6.565 per 1,000 cubic feet.