US benchmark West Texas Intermediate for March delivery rose 27 cents to USD 53.05 while Brent crude for April gained 56 cents to USD 61.96 in late-morning trade.
Greek Finance Minister Yanis Varoufakis said late on Monday that he was confident of reaching a deal with the eurozone on overhauling the country's unpopular debt bailout programme in two days, despite crunch talks collapsing.
The new anti-austerity Greek government is aiming to win a six-month reprieve so it can renegotiate the terms of its 240 billion euro (USD 270 billion) bailout, which its says has damaged the economy.
But its 18 eurozone partners, led by Germany, insist that any change to austerity terms must pass within the current programme, which Athens refuses to continue.
"If no deal is reached, another emergency meeting will reportedly be held on Thursday," said London-based research house Capital Economics.
"But the two parties will surely need to publish a statement implying that some progress has been made in the meantime if they are to avoid a more adverse market reaction and convince the European Central Bank to allow Greek banks continued access to funds," it added in a commentary.
Analysts said dealers were also digesting comments by Kuwaiti Oil Minister Ali al-Omair that world crude prices have recovered 'faster' than expected and recent gains will likely hold.
"I think it will last... It started holding gains now and hopefully, in the second part of 2015, we will see better prices," Omair said.

Kuwait, a member of the OPEC cartel, is the world's 10th largest petroleum producer, according to US Energy Information Administration.
Crude has been on a roller-coaster for the past two weeks after prices fell by around 60 percent between June and January.

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