Oil prices edged up after early falls on Monday as parts of Asia returned from the Lunar New Year holiday, with Brent futures moving further away from $60 a barrel and U.S. contracts moving towards $51.

After early trading losses, both international Brent and U.S. WTI crude futures edged up on Monday in reaction to cautious optimism that an immediate return of a eurozone crisis over Greek debt was averted by a compromise between Athens and its creditors.

Benchmark Brent crude futures were trading at $60.39. at 0201 GMT, up 17 cents from their last settlement, while U.S. WTI crude was up 5 cents at $50.86 a barrel.

Despite the small rises on Monday, prices remain below last week's highs.

Following a steep fall from June 2014 to six-year lows, oil prices recovered around a third of their value since mid-January, with benchmark Brent contracts jumping almost $20 a barrel to $63 a barrel last week as traders closed long-standing short positions in reaction to a falling U.S. rig count.

Yet many analysts said the price rise was overblown as record U.S. inventories and slowing demand around the world left oil markets oversupplied.

"U.S. crude oil prices slipped, as markets finally digested another rise in U.S. crudeinventories, which offset another week of oil rig count declines," ANZ bank said on Monday.

Although both U.S. WTI and international Brent prices dipped in the past week, American contracts have fallen more sharply largely in response to the record inventories.

This has pulled WTI's discount on Brent to over $9.50 a barrel, up from parity and even a short-lived premium late last year.

Yet analysts said they expected U.S. prices to recover later this year, once the falling rig count translates into lower output.

"Lower U.S. drilling activity will impact U.S. production later this year," BNP Paribas said in a note over the weekend.

"While the supply loss will be limited, it will occur at a time when global oil fundamentals are becoming far more balanced, and will contribute to improved price sentiment in 2H15."

Although most of the region is back from the Lunar New Year, markets in mainland China do not reopen until Wednesday.