New York's main contract, light sweet crude for delivery in November, added ten cents to $58.60 per barrel in electronic deals before the official opening of the US market.
In London, Brent North Sea crude for December delivery eased 12 cents to $60.75 per barrel in electronic trading.
The Organisation of Petroleum Exporting Countries, which produces just over a third of the world's oil, earlier said on Friday that it would cut current production by 1.2 million barrels per day (bpd) to 26.3 million bpd from November 1.
The announcement, which followed a special meeting in the Qatari capital of Doha, came after Opec members had suggested that the cartel would carry out a cut of one million bpd in a bid to shore up flagging crude prices.
Some ministers said a further cut of 500,000 bpd could follow when Opec next meets in Abuja in December to address high fuel stocks in consumer countries, particularly the US.
Mohammed bin Dhaen al-Hamili, UAE oil minister, made the announcement at a news conference in Doha.
He did not specify the amount of production that each member country would cut, but said the reductions will affect all countries except Iraq. It is to take effect on November 1.
The cuts will come from actual production levels, he said, and are more than the one million barrels a day being called for earlier by cartel members.
Opec is currently producing about 29.5 million barrels of oil per day.
Prices have declined more than 25 per cent since mid-July.
"The credibility of Opec is at stake," Chakib Khelil, Algeria's energy and mines minister, said before the meeting that began on Thursday and ended in the early hours of Friday.
After the meeting, Khelil said all 10 Opec members subject to quotas would participate in the cut.
Only Iraq, struggling to get its oil industry back on its feet after war and Western sanctions, was exempt.
"Everybody has a share," Khelil said.
Ali Al-Naimi, Saudi Arabia's oil minister, said the world's leading exporter fully supported the plan to cut supplies and he indicated that further cuts may be made.
"This is not the end of the road," he said.