Brent crude settled at $79.55 a barrel, losing 51 cents, or 0.6%. U.S. West Texas Intermediate crude settled at $74.37 a barrel, shedding 39 cents, or 0.5%.
In North Dakota, the third-largest oil-producing U.S. state, some oil output came back online after shutting because of extreme cold, the state's pipeline authority said. However, output was still down as much as 300,000 bpd.
Persistent weakness in U.S. gasoline demand has also hit oil prices, said John Kilduff, partner at Again Capital LLC.
While U.S. crude stocks dropped by 6.67 million barrels last week, gasoline inventories jumped by 7.2 million barrels, according to market sources citing American Petroleum Institute figures. Official U.S. government data is due on Wednesday.
Rising production elsewhere further pressured prices.
Norway's crude production rose to 1.85 million barrels per day (bpd) in December, up from 1.81 million bpd the previous month and beating analysts' forecasts of 1.81 million bpd, according to the Norwegian Offshore Directorate (NOD).
In Libya, production at the 300,000 bpd Sharara oilfield restarted on Jan. 21 after the end of protests that had halted output since early this month.
"You've got the geopolitical pressures that aren't enough to really rally the oil market, but they're enough to keep the market from bottoming out of the range," said Bob Yawger, director of energy futures at Mizuho Bank.
Crude prices rose by around 2% on Monday after a Ukrainian drone strike on Novatek's Ust-Luga Baltic fuel export terminal near Russia's second city St Petersburg raised supply concerns.
In the Middle East, tensions rose after U.S. and British forces carried out a second joint round of strikes on Houthi positions in Yemen.
Additional reporting by Robert Harvey and Noah Browning in London, and Emily Chow and Trixie Yapp in Singapore; Editing by Kevin Liffey, David Gregorio, Christina Fincher and Deepa Babington
