Oil prices eased in Asian trade on Monday, falling for a second session on concerns about the outcome of an emergency eurozone meeting later in the day on the Greek debt crisis and worries about oversupply.

Prices were up, though, from early lows after a European Commission official tweeted the latest proposal from Greece was a "good basis for progress" in Monday's talks.

"On a 24 hour basis we'll see some volatility depending on what happens with Greece," said Ric Spooner, chief market analyst at Sydney's CMC Markets.

Brent crude for August delivery was down 16 cents at $62.86 a barrel as of 0323 GMT, after dipping as much as 52 cents when Asian markets opened. The benchmark lost $1.24 in the previous session.

Front month US crude was down 13 cents at $59.48 a barrel after finishing the previous session down 84 cents.

Greek Prime Minister Alexis Tsipras offered a new reforms package to foreign creditors on Sunday in an effort to avoid default this month on 1.6 billion euros in debt repayments to the International Monetary Fund.

Worries over high domestic US oil production, which has held around 9.6 million barrels a day - the highest level since the early 1970s, also weighed on oil prices, Spooner said.

US oil producers added a rig each in the Permian and Bakken shale basins last week, fuelling worries over high domestic oil output, even as the total number of active US rigs fell last week, data on Friday showed.

"My expectation for a price increase is fairly limited," Spooner said. "One way or another we are likely to see some production cuts. If we did see prices go up then OPEC would increase production and/or US producers would increase theirs as well."

Other analysts also continue to point to the overhang of supply in the market.

Ten 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, posing a worrying 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 when crude runs and gasoline demand fall seasonally," the note said.

And considering the prospects of new supply from Libya and Iran a lower price environment seems increasing likely, Morgan Stanley analysts said. – Reuters