By Julia Payne
Benchmark Brent crude oil rose $3.48 a barrel to a high of $63.54 before easing back to around $63.20 by 1450 GMT. In early trade, Brent had fallen below $60 when it looked as if oil exporters might not agree.
U.S. light crude rose $2.69 to a high of $54.18 a barrel before slipping to around $53.80.
Prices fell almost 3 percent on Thursday after the Organization of the Petroleum Exporting Countries ended a meeting in Vienna with only a tentative deal to tackle weak prices. Talks with other producers were held on Friday.
Oil prices have plunged 30 percent since October as supply has surged and global demand growth has weakened.
But Iran gave OPEC the green light on Friday to reduce oil output by around 0.8 million barrels per day from 2019 after finding a compromise with rival Saudi Arabia over a possible exemption from the cuts, an OPEC source said.
A Russian Energy Ministry source said Moscow was ready to contribute a cut of around 200,000 bpd and sources said other non-OPEC producers could contribute a further 200,000 bpd of output cuts, bringing an overall cut to 1.2 million bpd.
"(A cut of) 1.2 million bpd, if implemented promptly and fully, should be enough to largely attenuate, but not eliminate, expected implied global inventory builds in the first half of next year," BNP Paribas strategist Harry Tchilinguirian told Reuters Global Oil Forum.
"Given how much expectations were downplayed yesterday, this comes as a welcome surprise for the market," he added.
Oil output from the world's biggest producers - OPEC, Russia and the United States - has increased by 3.3 million bpd since the end of 2017 to 56.38 million bpd, meeting almost 60 percent of global consumption.
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