The El Sarir oil field was still unable to pump oil on Monday after a pipeline was attacked and set on fire.
Further supporting the market, Kuwait's oil minister said oil prices would continue to rise in 2015 as supply levels fell.
"Hopefully in the second half of 2015 we will see better prices," said the minister, Ali al-Omair.
Benchmark Brent futures traded at $61.93 a barrel, up 41 cents, by 1257 GMT. U.S. crude was up 20 cents at $52.97 a barrel. Trading volumes were reduced as U.S. markets remained closed for a public holiday.
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Oil markets rose strongly last week after another drop in the U.S. rig count, pushing Brent back above $60 a barrel for the first time since December.
The price of Brent crude has increased by more than 30 percent since January, supported by signs of lower oil industry spending. In January it hit $45.19, the lowest in almost six years, down from $115 last June.
Kuwait's Omair said the current oil surplus was now "definitely lower" than 1.8 million barrels per day.
"The big guessing game is whether we are now moving to a range from $60-68, or whether we're about to turn south again and head back below $60 or possibly $50," said Jeffries oil broker Christopher Bellew.
The loss of output from Libya comes as Iraq's southern oil exports have fallen sharply to below 1.5 million bpd in the first two weeks of February, shipping data tracked by Reuters showed.