Speaking in an unscheduled television address on Sunday, he said Greece had a duty to finish negotiations with the European Union and International Monetary Fund to exit its bailout accord next year.
But in an appeal to pro-European independents, he said he would be willing to widen his ruling conservative/center-left coalition if lawmakers supported the election of a new president.
The surprise announcement comes two days ahead of the second round of voting for president and follows a disappointing result for the government in the first round last week when it won less support than expected.
If the 300-member parliament does not choose a president by the third round of voting on Dec. 29, a general election will have to be held by early February, putting negotiations over Greece's international bailout agreement at risk.
Samaras, who still needs to win over another 20 votes from the independents and small parties, called on deputies to listen to "the voice of national interest and common sense" to elect his candidate Stavros Dimas and allow bailout talks to wrap up.
"Then, shielded economically and politically, we can find a suitable timeframe for national elections even at the end of 2015," he said.
Vassilis Economou, a pro-European independent whose intentions were being closely watched, welcomed the offer and called on other independents to back the government.
However the leftwing Syriza party, which wants to renegotiate the bailout, rejected the offer immediately as did the Independent Greeks, a small right-wing anti-bailout party which wants new elections.
"It's not possible," Syriza spokesman Panos Skourletis said. "Mr Samaras does not face the judgment of the Greek people."
The other small party expected to play a key role, the Democratic Left, said it would consider its response at a meeting in parliament on Monday.
Syriza has seen its opinion poll advantage narrow over the past few weeks but it still sits ahead of the ruling coalition with a lead of 3.6 points according to the latest poll on Saturday.
No clear result was expected in Tuesday's second round in parliament, when Dimas will need 200 votes to win. If the government cannot better its first-round score of 160, it will be seen as a major blow ahead of the decisive final round next week, when the threshold for victory drops to 180.
