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Brent futures were $1.01 higher at $110.07 per barrel at 0817 GMT.
Gunmen from a former rebel faction kidnapped Libyan Prime Minister Ali Zeidan on Thursday in reprisal for the government's role in the US capture of a top al Qaeda suspect.
Libya's oil output has risen to 700,000 barrels per day, after falling at mid-year to its lowest since the country's 2011 civil war as strikes, militias and political activists blocked most oilfields and ports.
Since violence broke out, the government's fledgling army and police force have struggled to deal with armed protesters.
Investors were looking to when the rest of the oil production - total capacity is over 1.5 million bpd - would be back on stream.
"Markets were not anticipating a quick restart of the 0.9 million bpd missing crude oil production from Libya but a restart was a bearish flag," said Olivier Jakob, analyst at Petromatrix in Zug, Switzerland.
"That flag can now be pushed further away in time."
US oil was up 43 cents at $102.04 per barrel.
FISCAL PROGRESS
Commodity and equity prices were also supported on signs of progress in Washington on ending the US fiscal stalemate and averting a possible debt default.
US Republicans were looking into a short-term hike in the government's borrowing authority to buy time for talks on broader policy issues, a Republican leadership aide said on Wednesday.
Also supporting prices was renewed worry about supply from Nigeria.
Shell Nigeria
"Better supplies out of Nigeria and Libya were another bearish influence but this seems not to be the case anymore," said Christopher Bellew, broker at Jefferies Bache.
Oil recovered losses from the previous session after US crude stocks rose by 6.8 million barrels in the week to October 4, well above forecasts by analysts of a 1.5 million barrel increase.
Over the past three weeks, crude stockpiles have increased by a total of 14.9 million barrels, according to the US Energy Information Administration, the biggest three-week increase since April 2012.
