Antonis Samaras told German daily Bild that Greece needed “breathing space”.
He will meet Jean-Claude Juncker, the head of the Eurogroup of finance ministers later, and the French and German leaders later this week.
At issue is whether Greece has done enough to receive its next 31.5 billion-euro bailout payment.
Failure to unlock the funds could lead to Greece defaulting on its vast public debt and possibly leaving the euro.
Antonis Samaras is under pressure to show Greece can fulfill its commitment of 11.5 billion euros in public spending cuts within two years in order to qualify for the money.
At the talks with Jean-Claude Juncker, he is expected to float the idea of Greece being given a two-year extension to the deadline.
He will argue that Greece has lost time because of elections this year, and that it should be allowed to move more gradually in order to ease the economic pain felt by the Greek people.
“Let me be very explicit: we demand no additional money. We stand by our commitments,” Antonis Samaras told German tabloid Bild in an interview published on Wednesday.
“But we have to kick-start growth in order to cut our deficit. All that we want is a little <<breathing space>> to revive the economy quickly and raise state income.”
However, a government source says Antonis Samaras will not press the issue too hard, fearing it might cause bad blood with the group of lenders that monitors Greece’s bailout.
Yannis Varoufakis, professor of economics at the University of Athens, said Antonis Samaras was “profoundly, deeply and sadly wrong. Greece does not need more breathing space. It is not breathing at all.”
He said the solution Europe had implemented to tackle Greece’s insolvency crisis was a “very silly one” – providing gigantic loans “on condition of austerity measures that would shrink the national income from which that huge loan would have to be repaid”, requiring yet more loans and more austerity.
Antonis Samaras goes on to meet German Chancellor Angela Merkel on Friday, and French President Francois Hollande on Saturday.
The “troika” – the European Union, the European Central Bank and the International Monetary Fund (IMF) – is expected to report on Greece’s progress next month.
Eurozone leaders have so far resisted any move to soften the bailout conditions.
Especially in Germany, the eurozone’s richest country, the government is under pressure not to make any more concessions.
On Monday, German Foreign Minister Guido Westerwelle insisted Athens must press ahead with the terms already agreed.
The heavily-indebted country has received two massive EU and IMF bailouts – one for 130 billion euros this March and one for 100 billion euros in May 2010 – to allow it to continue payments on its vast public debt and stay in the eurozone.
Cuts in public spending, benefits, pensions and public sector salaries imposed as a result of both loans have led to severe economic hardship, and Greece remains mired in recession.
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