Oil prices rose above $63 a barrel on Monday in response to new proposals from Greece that the European Union welcomed as a basis for progress at talks to try to stave off a default that could cause turmoil in financial markets.
But high levels of global oil production and stocks continued to exert pressure on crude prices.
Brent crude for August delivery was up 30 cents at $63.32 a barrel by 0822 GMT, after falling nearly 2 per cent on Friday over worries about a potential Greek debt default.
Front month U.S. crude was 44 cents higher at $60.05 a barrel.
Prices rebounded from early lows after the EU's positive response to Greek Prime Minister Alexis Tsipras's latest proposals to try to resolve the country's debt crisis.
"Hopes that agreement could be reached in the debt dispute with Greece at today's EU summit are lending buoyancy to oil prices as the new week begins," Commerzbank analysts said in a note to clients.
But a crude oil overhang, particularly in the Atlantic basin, is limiting gains.
Around 10 million barrels of unsold crude, mainly from Nigeria, are held in offshore storage despite strong summer demand, Morgan Stanley said in a research note on Monday, potentially creating a negative outlook for oil in the second half of the year.
"If there are this many challenged cargoes in this strong demand environment, we worry about the outlook for physical oil this fall (autumn) when crude runs and gasoline demand fall seasonally," the note said.
High domestic U.S. oil production, which has held up at around 9.6 million barrels a day, the highest level since the early 1970s, continued to weigh on oil prices.
U.S. oil producers added a rig each in the key Permian and Bakken shale basins last week, fuelling worries over high domestic oil output, even as the total number of active U.S. rigs fell last week, data on Friday showed.
Although U.S. oil production was expected to decline slightly between the second and third quarters of 2015, output
"would continue to grow in 2016 by 150,000 barrels per day at the current rig count," Goldman Sachs said in a note.
If a standoff between six powers and Iran over its nuclear program is resolved by a June 30 deadline, this could lead to an easing of sanctions on the country, which could ultimately release more oil into the market, adding to supply pressures.
Brent crude could break support at $60.50 per barrel and fall further towards its next support at $51.09 over the next quarter, Reuters technical analyst Wang Tao said.
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