Armed factions have blocked production at the western Libyan oilfields of Sharara and Wafa, reducing output by 252,000 barrels per day (bpd), about a third, said a source at the National Oil Corp (NOC).
NOC has declared force majeure on crude loadings from those oilfields.
Brent crude rose 58 cents, or 1.14 percent to settle end $51.33 per barrel. West Texas Intermediate (WTI) crude ended the session 64 cents, or 1.34 percent higher at$48.37 a barrel. Both benchmarks were up about 2 percent at their session highs.
"The closure of two Libyan oil fields is supporting the market today with the timing of a potential restart uncertain after militias in western Libya shut key pipelines," Tim Evans, an energy futures specialist at Citi Futures said in a note.
"Past outages have ranged from a few days all the way up to two years, although the need for oil revenues will be a strong incentive to negotiate a pipeline restart sooner rather than later."
Iranian Oil Minister Bijan Zanganeh said the deal between OPEC and non-OPEC producers to cut output and reduce the global crude glut is likely to be extended beyond June. Russia, a non-OPEC member, is seen as a wild card. However, Russia and Iran signed a joint statement saying they will keep cooperating to reduce output.
Non-OPEC member Azerbaijan also said it was ready to join an extension of the deal.
Major oil traders gathered in Switzerland this week said they expected the output cuts to be extended, providing Russia complies.
Still, resurgent US oil production and record domestic crude inventories have kept pressuring oil prices. Analysts polled by Reuters predicted that data will show US crude oil stocks rose 1.2 million barrels in the latest week.
Data from the American Petroleum Institute is due at 4:30 p.m. The US Energy Information Administration reports at 10:30 a.m. on Wednesday.
Saxo Bank Head of Commodity Strategy Ole Hansen said "an increase of more than 322,000 barrels will see Cushing hit a record".
Rising stocks at the Cushing, Oklahoma, storage and delivery point for WTI tend to depress the price of the US benchmark.
Rising domestic production has pushed WTI's discount to Brent to its steepest since the United States lifted a ban on exports in late 2015. Analysts and traders said they expect US crude exports to pick up.