Zueitina is 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 below 500,000 barrels per day (bpd), officials say, a third of what the country pumped before 2010.
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Investors have moved heavily into oil over the last few weeks as prices have recovered from a slump in January. Crude prices have now risen 50 percent in just over three months.
Hedge funds and money managers raised 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 its northern neighbor, Saudi Arabia, or other Middle East Gulf producers.
The oil market is well supplied, with producers of the Organization of the Petroleum Exporting Countries pumping almost 2 million bpd more than demand for their oil.
OPEC meets next month to discuss production policy but analysts see little chance that it will restrain output as members battle for market share.
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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.
The U.S. Energy Information Administration will publish it official report on U.S. oil inventories on Wednesday.