US light crude edged up 8 cents to $61.17 a barrel, after gaining 43 cents on Thursday. London Brent crude traded 6 cents up at $59.20 a barrel.
"Though there seems to be a lot of crude around, the long-term view is bullish," said Tony Nunnery at Mitsubishi Corp in Tokyo. "The US Northeast will get colder and people may be concerned with middle distillate supplies."
Demand for distillate fuels such as heating oil peaks in the Northern Hemisphere's winter. Temperatures in the US Northeast, the world's biggest heating oil market, were expected to be 3 to 8 degrees Fahrenheit below normal until the weekend.
A rise in US fuel demand could come while the recovery of oil and natural gas production from the storm-battered Gulf of Mexico home to more than a quarter of US domestic output remains at a crawl.
Some 1.022 million barrels per day (bpd) or 68 percent of the Gulf's crude output stayed shut on Thursday, along with 5.559 billion cubic feet per day or nearly 56 percent of gas output, the US government said, a thin improvement from Wednesday.
Dampening hopes of recovery, the US Interior Department said on Thursday that energy operations in the Gulf of Mexico would not return to normal until late March next year.
A larger-than-expected fall last week of 1.6 million barrels in US distillate stocks including heating oil and diesel kept alive concerns over winter supplies, despite a large 4.4 million-barrel build in crude inventories.
Demand for distillate fuels was 1.4 percent lower in the last four weeks compared to the same period last year, US government data showed this week.
Oil markets are carefully watching for any signs that high prices are hurting demand. "Sales show no clear evidence of demand destruction," said Deutsche Bank in an analysis on the results of Exxon Mobil Corp, the world's largest oil company, which on Thursday posted quarterly profits up 75 percent on the year at $9.9 billion.
Implied oil demand from China, the world's second-biggest oil consumer, jumped 9.7 percent in September, the highest since January, based on Reuter's calculations.
But China's demand has slowed overall this year after a 15 percent demand growth last year-helped fuel oil's rally. Top Asian refiner Synoptic Corp said on Friday it would delay some of its refining projects in line with slower demand in China.
"We would like to limit the growth of our refining capacity, now that market demand for refined oil products has fallen back to normal levels," Chief Financial Officer Zhang Jared said.
A strike threat at Europe's largest refinery could further strain a stretched global refining system. Workers at Shell's 418,000-bpd Pernis plant in Rotterdam threatened to walk out on Monday in a dispute over pensions.
It is not yet clear whether the action will affect plants around Antwerp. Esso Benelux said it expected no impact on its 246,000-bpd plant.