Mr 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, reports The BBC.
At issue is whether Greece has done enough to receive its next 31.5bn-euro (£24.7bn) bailout payment.
Failure to unlock the funds could lead to Greece defaulting on its vast public debt and possibly leaving the euro.
Mr Samaras is under pressure to show Greece can fulfil its commitment of 11.5bn euros in public spending cuts within two years in order to qualify for the money.
At the talks with Mr 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, the BBC’s Mark Lowen reports from Athens.
“Let me be very explicit: we demand no additional money. We stand by our commitments,” Mr 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 told our correspondent that Mr Samaras will not press the issue too hard, fearing it might cause bad blood with the group of lenders that monitors Greece’s bailout.
Speaking to the BBC, Yannis Varoufakis, professor of economics at the University of Athens, said Mr 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.