Brent for March settlement climbed 16 cents to end the session at $67.78 a barrel on the London-based ICE Futures Europe exchange.
"You're so long this market at this point, you could certainly get more interest at these levels", said Rob Haworth, senior investment strategist at U.S. Bank Wealth Management.
Despite this, USA production is expected to break through 10-million barrels a day very soon, largely thanks to soaring output from shale drillers.
Late Tuesday, trade group the American Petroleum Institute will release figures on domestic petroleum supplies, followed by Wednesday's EIA figures.
OPEC is cutting output by even more than it promised and the restraint is reducing oil stocks globally, a trend most visible in the United States, the world's largest and most transparent oil market.
This week's supply reports from the American Petroleum Institute and the USA government's Energy Information Administration are predicted to reveal that us crude stocks dropped by 4.1 million barrels, an eighth week of decline.
Crude oil futures continued to surge Tuesday on expectations the global oil market will soon re-balance.
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There is no sign yet that OPEC is prepared to relax its supply restraint.
"Led by USA production, particularly the Permian Basin, and now new oil sands projects in Canada, non-OPEC production is forecast to continue growing through the end of 2019", John Conti, the agency's acting administrator, said in a statement.
"The U.S. oil price is now into a range that is anticipated to attract increased shale oil production", said Ric Spooner, chief market analyst at CMC Markets in Sydney.
Nationwide output will average 10.85 million barrels a day next year and 10.27 million this year, both surpassing the prior record of 9.6 million pumped in 1970, the Energy Information Administration said in its monthly Short-Term Energy Outlook, which included the first estimates for 2019.
The report also noted that the North Sea Brent barrel stands at $64 per barrel, which is the highest it has been since November 2014, the start of the oil price crisis.
Adding to the positive sentiment, analysts expect global economic growth to lead to higher demand for oil. Only Russia and Saudi Arabia produce more. "But for now, the bullish trend remains intact as prices remain above key supports".