US benchmark West Texas Intermediate for August delivery was up 13 cents at USD 52.87 barrel compared with Friday's close.
Brent North Sea crude for August slipped 22 cents to stand at USD 58.51 a barrel in late London deals.
Despite earlier optimism, there is little possibility that Iran and major powers will agree a historic nuclear deal before Monday night's deadline, an Iranian source told AFP.
Asked if reaching a deal today was now out of the question, the source close to the Iranian delegation said that there was only a "low chance".
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Rouhani's appearance is scheduled for around 10:00 pm (1730 GMT) the official said, noting that the president would talk about the negotiations taking place in Vienna.
Any deal to curb what the West suspects as Iranian efforts to build an atomic bomb will result in the lifting of punishing economic sanctions, allowing the country to resume oil exports.
More Iranian oil however will add to a supply glut, which has depressed prices.
OPEC today revised upward its forecast for global crude oil demand growth for this year and also predicted a further increase for 2016 as the world economy picks up again.
In its July monthly report, OPEC said it expected global oil demand to increase by 1.28 million barrels per day -- some 100,000 barrels more than in its June estimates.
OPEC's latest figures differ from those of the International Energy Agency, which indicated last week that world oil demand growth would fall to 1.2 million barrels a day in 2016, from 1.4 million this year.