US West Texas Intermediate futures settled up 44 cents, or 0.8 percent, to $57.04 a barrel.
Brent crude futures settled at $62.44 a barrel, the same settlement as Wednesday.
Prices have been supported by an outage on the Forties crude pipeline that was expected to last several weeks.
"At present you can't ignore the impact of the Forties pipeline outage," said John Kilduff, partner at Again Capital Llc in New York, "It's a significant amount of oil that the market is going to miss and is missing. And it's almost surprising it's not generating more support."
A reformer was shut on Thursday after a fire in the East Plant at Citgo Petroleum Corp's 157,500-bpd Corpus Christi, Texas, refinery, said sources familiar with plant operations.
The Paris-based International Energy Agency (IEA) expects the oil market to have a surplus of 200,000 barrels per day (bpd) in the first half of next year before reverting to a deficit of about 200,000 bpd in the second half. That means 2018 overall should show "a closely balanced market".
The IEA said US crude output next year would increase by 870,000 barrels per day, up from its November forecast of 790,000 bpd.
With cash pouring into the US shale oil industry, the United States is on track to deliver up to 80 percent of the world's oil production gains through 2025, the IEA estimates .
Yet after lows of $56.09 earlier in the day for US crude and $62.01 for Brent crude, both grades had rallied again by settlement.
"The market seems to have digested (the IEA report) and is turning its attention to the fact that we're beginning to tighten," said Gene McGillian, director of market research at Tradition Energy.
A fall in US crude inventories last week also lent some support. Stocks fell by 5.1 million barrels in the week to Dec. 8, the fourth consecutive week of decline, to 442.99 million barrels, the lowest since October 2015.
The front month of the US crude curve for February and March remains in backwardation. Backwardation, in which the futures contract trades below the crude oil's expected spot price at the contract's maturity, is an indicator of a tight market.