Brent crude futures gained 25 cents, or 0.43%, to $58.71 a barrel by 1025 GMT, having earlier hit their highest since Feb. 21 last year.
U.S. West Texas Intermediate (WTI) crude futures climbed 31 cents, or 0.56%, to $56 a barrel after reaching its highest settlement level in a year on Wednesday.
"Supporting factors outweigh negative developments at the moment," said PVM Oil Associates analyst Tamas Varga, citing high compliance with OPEC+ production cuts and its declared target to accelerate stock depletion.
"The extra 1 million barrel per day (bpd) Saudi cuts that started this month imply further stock draws until at least the end of the first quarter," Varga added.
The Organization of the Petroleum Exporting Countries (OPEC) and allies, a group known as OPEC+, extended its oil supply pact at existing levels on Wednesday, suggesting that producers are happy the cuts are draining inventories while uncertainty remains over the outlook for a recovery in demand as the COVID-19 pandemic lingers.
A document seen by Reuters on Tuesday showed that OPEC expects output cuts to keep the market in deficit throughout 2021, even though the group reduced its demand forecast.
The market was further bolstered by news that Democrats in the U.S. Congress took the first steps toward advancing President Joe Biden's proposed $1.9 trillion coronavirus aid plan.
Also supporting prices, U.S. crude oil stockpiles fell by 994,000 barrels last week to 475.7 million barrels, the lowest level since March, the U.S. Energy Information Administration said on Wednesday. Analysts in a Reuters poll had forecast a rise of 446,000 barrels.
In a separate development, the United States has filed a lawsuit to seize a cargo of oil it says came from Iran rather than Iraq, as stated on the bill of lading, contravening U.S. terrorism regulations.