Brent crude moved back toward a four-month high near $110 a barrel following last week's sell-off, while U.S. crude hit the highest level in six sessions to above $107.
Labor unrest in Libya has forced oil output to its lowest since the 2011 civil war, with the country's total oil production well below 500,000 barrels per day (bpd) from 1.3 million bpd in June.
This sparked fear of a possible supply shortfall in the northern hemisphere and boosted prices, analysts said.
Libya's state National Oil Corporation said in a statement to shippers that it could not provide September loading schedules, normally due by now, as on-again, off-again strikes paralyse its ports.
"The question is how long does it last. Today it's manageable."
Richard Mallinson, chief policy analyst at London-based consultancy Energy Aspects, told Reuters Global Oil Forum, that output was around 400,000 bpd and exports at around 300,000 bpd. Libya has the capacity to produce around 1.6 million bpd.
Maintenance work at Iraq's key southern oil export hub is also expected to cut supplies by 500,000 bpd in September, lending further support to prices in the medium term.
Front-month Brent crude oil futures for September delivery rose 85 cents to settle at $109.82 a barrel after touching an intraday high of $110.06, its highest since it hit a four-month high of $110.09 on Aug. 2.
Brent rose back above its 200-day moving average on Monday at $108.17, a technical marker watched by traders. The contract also fully breached the short-term 10-and-15 day moving averages on Tuesday.
Trading in CME Group Inc's New York Mercantile Exchange Brent crude oil contract set a record on Tuesday, the exchange said, at 104,839 contracts, eclipsing the previous high of 90,390 reached late last week.
Higher oil prices are already taking a toll on oil refiners in Europe, who are expected to cut processing rates by around 500,000 bpd this week on poor profit margins.
In the United States, front month crude oil futures rose 72 cents to settle at $106.83 a barrel after trading as low as $105.56 during the session. U.S. crude's discount to Brent settled at $2.99 a barrel.
A warning by the U.S. National Hurricane Center that a tropical wave might become a cyclone in the oil-producing Gulf of Mexico supported prices.
Also supporting prices are expectations that data will show a drawdown in U.S. crude oil supplies.
U.S. crude oil and gasoline stockpiles probably fell last week, according to seven analysts polled by Reuters on Monday. The poll, ahead of weekly inventory reports from the American Petroleum Institute and the U.S. Energy information administration, forecast a 1.5 million barrels drop in crude oil inventories and a 900,000-barrel fall in gasoline stockpiles. Reuters will release the API data on Tuesday at 4:35 p.m. EDT