US January crude oil futures slipped 26 cents to $61.04 a barrel by 0635 GMT after having briefly matched Friday’s $61.50 peak, the highest since early November.
London January Brent crude was down 34 cents at $59.10 a barrel.
Oil prices rose more than 3 percent on Monday, closing at its highest level since Nov. 3.
"People are looking at the cold weather in the US and realise that OPEC will be cutting production," said Tetsu Emori, chief commodities strategist at Mitsui Bussan Futures.
The Organization of the Petroleum Exporting Countries, which has been pumping above its formal ceiling of 28 million barrels per day (bpd), agreed on Monday to rein in excess output, but some core members looked set to keep pumping unabated.
"We are trying to do maximum production," Kuwati Oil Minister Sheikh Ahmad al-Fahd alSabah, also OPEC’s president, said on Tuesday. He had said on Monday that he thought the cartel would keep pumping 28.2 million bpd, despite the agreement.
"I don’t think it (production) is going to change," said UAE Oil Minister Mohammed bin Dhaen alHamli.
And late on Monday top exporter Saudi Arabia told its global oil customers that it would keep most crude supplies unchanged in January from the month before, although one refiner in South Korea said it had received notice of a tiny cut in supply.
The cartel will meet again on Jan. 31 in Vienna to discuss policy for the second quarter, when demand wanes.
Sheikh Ahmad said on Tuesday that the cartel’s decision to call a meeting next month may have given the market a signal that it would cut output if demand appeared to be slackening.
US crude prices are likely to remain steady in a range of $55-$65 a barrel until the next OPEC meeting, said Akihiko Tembo, president of Japan’s third largest refiner Idemitsu Kosan Co.
Prices were also buoyed by forecasts for temperatures in the US Northeast — the biggest heating oil market in the world — to dip below normal for most of the week, driving up demand.
"Weather forecasters are pencilling in more cold weather for the United States, so demand for heating, and the energy that fuels it, will be stronger," said Tobin Gorey, commodity analyst at the Commonwealth Bank of Australia.
Analysts said the market was also keenly watching US data on stocks of crude oil and distillates.
US commercial crude oil stocks probably fell 1.0 million barrels for the week to Dec. 9, according to a Reuters survey of analysts ahead of data from the US Energy Information Administration (EIA) on Wednesday.
Distillate stocks, which include heating oil, were forecast to have risen 100,000 barrels, on average, while gasoline stocks were expected to show a 1.2 million barrel build.
In the week to Dec. 2, US crude, distillates and gasoline inventories each rose by 2.7 million barrels, supported by higher imports.
