At the same time, speculation is rising that American drillers will put more rigs to work next year as oil strengthens. The US expects production to top 10 million barrels a day in the coming year.
According to the EIA, U.S. crude stocks fell last week as refineries hiked output, while gasoline and distillate inventories rose.
Inventories are now down by nearly 20% from their historic highs last March and well below this time a year ago or in 2015.
Crude oil were lower on Friday as expectations OPEC and other producers will extend their production cut agreement were offset by forecasts USA output will continue to grow with prices holding near 28-month highs.
U.S. West Texas Intermediate (WTI) crude futures were at $60.16 a barrel at 0210 GMT, up 33 cents or 0.5 percent from their last close.
The survey of 32 economists and analysts forecast Brent crude would average US$59.88 a barrel in 2018, up from the US$58.84 forecast in the previous monthly poll.
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WTI prices were further boosted by a fall in United States commercial crude storage levels, which dropped by 4.6 million barrels in the week to December 22 to 431.9 million barrels, according to the EIA.
This week, WTI broke through $60 a barrel for the first time since June 2015, while Brent breached $67 for the first time since May 2015.
There are also expectations in the market that OPEC's next meeting on November 30 will agree to extend cuts beyond the current expiry date in March 2018.
USA output has surged overall this year, hitting a 46-year high in October when producers pumped 9.6 million barrels a day, according to federal data.
Pipeline outages in Libya and the North Sea have also been supporting oil prices, although both these disruptions are expected to be resolved by early January.