New York's main contract, light sweet crude for July, gained $1.19 to $101.93 a barrel.
London's Brent North Sea crude for delivery in July rose $1.72 to $119.57 a barrel.
OPEC's heated meeting in Vienna on Wednesday resulted in the cartel's official output target remaining at 24.84 million barrels per day (bpd), where it has stood since January 2009.
That announcement sent oil prices rocketing two dollars on Wednesday. Traders had speculated that the 12-nation Organization of the Petroleum Exporting Countries (OPEC) would boost the production quota to help cool oil prices and in turn boost economic recovery.
"Crude is rallying because of OPEC... failing to reach an agreement on higher output levels," Victor Shum, a Singapore-based analyst at Purvin and Gertz international energy consultancy, told AFP.
"In the long term, the oil market is fundamentally bullish with demand growth going forward, and so the OPEC group is going to have to supply more output."
Supply-side worries include the conflict in OPEC member Libya, the analyst added.
Output by Libya, a key crude-exporting nation which was producing about 1.7 million bpd before the rebellion broke out in mid-February, has been choked since the revolt began.
But on Thursday, the minister of oil and finance in the Libyan rebel council, Ali Tarhoni, said the rebels would start producing 100,000 bpd "soon."
He said "we are hoping soon," when asked when the rebels would start producing oil from the eastern fields under their control. "One hundred thousand barrels per day or so," he added.
According to the International Energy Agency (IEA), Libya's exports averaged 1.49 million bpd before the uprising, with 85 per cent of that going to Europe.
Regarding OPEC, the IEA said it was "disappointed" by the cartel's output decision and urged producers to pump more anyway to avoid higher oil prices.
The IEA, representing the interests of industrialised nations, estimates that actual OPEC production stood at 26.15 million bpd in April, giving an overshoot of about 1.3 million bpd. But even such extra output is not seen as sufficient to meet future demand.
The OPEC meeting meanwhile exposed deep divisions within the cartel. Kuwait, Saudi Arabia, Qatar and the United Arab Emirates had called for a boost of 1.5 million barrels to the ceiling, but fellow members rejected the idea.
Analyst Jason Schenker, at US-based Prestige Economics, said that the decision would not change a great deal.
"I think fundamentally it's not going to change the supply situation. I think (OPEC's main producer) Saudi Arabia is going to produce additional oil regardless.
"In the short-term this (meeting) may be interpreted as bullish but the truth is that the market is going to be well-supplied," he added.
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