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New York's main contract, West Texas Intermediate light sweet crude for July delivery, expired with a close at $93.26 a barrel, a gain of 25 cents from Friday.
By contrast, London's Brent North Sea crude for August delivery fell $1.52, settling at $111.69 a barrel.
The New York benchmark contract's small rise nevertheless marked a rebound from early in the session, when it had hit a fresh February low.
"Oil prices continue to get pressured as the Greece bailout is still not settled. Hopes that a meeting over the weekend would make the Greek crisis go away were wishful thinking," said Phil Flynn at PFG Best Research.
Rich Ilczyszyn at futures brokerage Lind-Waldock said the WTI gain may be technical after recent sharp falls in oil prices as investors worry that Greece may have to default on its debt in mid-July.
"I?m still bearish on oil but this is a small attempt to stage a bit of a rally," Ilczyszyn said.
"We hit a very specific technical level -- a lot of big traders are recommending to buy," he explained.
He said the market also was "bouncing" with the equity markets.
The WTI contract, which had plunged $6 last week, sank to $91.14 in early trading, its lowest level since late February.
But it climbed in late trade as Wall Street stock markets headed higher.
The Greek debt drama continued to hang over financial markets after eurozone financial ministers over the weekend gave Greece an ultimatum: the government has two weeks to adopt drastic new austerity measures, or face the prospect of no emergency funds to avert default.
"Questions remain on whether or not Greece will get its much needed influx of cash and this is raising default fears once again. Not to mention contagion. We see demonstrations in Spain because of dismal economic prospects," said Flynn.
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