, hampering exports , Reuters reported.
Zueitina was one of the few Libyan ports still exporting oil as many others have closed due to fighting or disruptions at oilfields since the ousting of former dictator Muammar Gaddafi.
Libyan oil output is now less than 500,000 barrels per day (bpd), officials say, a third of what Libya pumped before 2010.
A strong dollar also weighed on oil, making the commodity more expensive for holders of other currencies.
Brent crude oil was up 10 cents at $66.55 a barrel by 0825 GMT, after touching a 2015 intra-day high of $67.10 on Monday.
U.S. crude oil was up 5 cents to $58.98 a barrel.
"Oil is taking a breather after the latest rally," said Carsten Fritsch, senior oil analyst at Commerzbank in Frankfurt.
"Momentum is key here," Fritsch added. "The rally is feeding itself with a lot of money looking for buying opportunities."
Hedge funds and other money managers raised their bets on rising Brent prices to another record, data showed on Monday, pushing net long positions to their highest since official exchange records began in 2011.
Civil war in Yemen has kept the oil market on edge, underpinning prices due to the risk of disruption to oil supplies from the country's northern neighbour, Saudi Arabia, or other Middle East Gulf producers.
The Saudi foreign minister said on Monday the Saudi-led Arab alliance bombing Houthi fighters in Yemen might call a truce in some areas to allow humanitarian supplies in.
But the oil market is extremely well supplied with producers of the Organization of the Petroleum Exporting Countries pumping almost 2 million bpd more than current demand for their oil.
OPEC ministers meet next month to discuss production policy but analysts see little chance that they will retrain output as they battle for market share.
Investors awaited data on U.S. commercial crude oil stocks.
A Reuters poll on Monday said commercial crude stocks may have risen by nearly 2 million barrels last week, building for a record 17th straight week.