The leadership crisis has raged for more than a week after elections gave no party a majority in parliament.
President Karolos Papoulias met the heads of the conservative New Democracy, socialist PASOK and Democratic Left parties today in the eighth day of talks to resolve the deadlock.
The leaders said the president had suggested creating a government of technocrats or “personalities,” and will convene another meeting with the heads of more parties tomorrow to seek support.
If no deal can be reached, elections must be called for next month.
As uncertainty in Greece continues, Taoiseach Enda Kenny has shot down calls for the referendum on the European fiscal treaty to be postponed.
He rejected claims from a group of independent politicians that uncertainty in France and Germany, and potential revisions to the treaty text mean it is too soon for the Irish people to cast their vote.
“The date is fixed for May 31,” he said.
“The reason it’s important we leave it at May 31 is that it allows us to send out a very clear signal of certainty from our people, about our country.”
The Taoiseach said sticking to the original referendum date shows potential investors that Ireland is serious about being part of the eurozone.
“We can send out a very clear and strong signal about where Ireland is headed,” Mr Kenny added. Independent TDs had called for the postponement.
His comments come as Greece’s continued participation in the euro remains in serious doubt.
The conservative New Democracy party won the May 6 election, but the poll failed to produce an outright winner. Alexis Tsipras, leader of the second-placed, left-wing Syriza party, has refused to join a coalition, demanding that the terms of an international bailout be scrapped or radically renegotiated.
Many see fresh elections as inevitable. But a new poll could see anti-austerity parties gaining more support and prompt a rift in 17-nation eurozone and raise the risk of a Greek exit from the shared currency.
The president will meet the heads of six of the seven parties that won parliamentary seats in the May 6 election, socialist PASOK leader Evangelos Venizelos said after talks with him and the heads of conservative New Democracy and the small Democratic Left parties.
Mr Venizelos did not list the extremist right-wing Golden Dawn party among those invited. Golden Dawn’s surge in popularity in the election has caused consternation amongst many Greeks, and the other parties have been reluctant to have any dealings with its leaders.
“The effort to form a government continues. All three of us political leaders agreed that it is absolutely necessary to have the broader support of political parties to attain such a viable government,” New Democracy leader Antonis Samaras said after the meeting with the president.
“The people have given us a very clear mandate: We must try, as far as we can, all of us together, to shape this new government. Everyone must now assume their historic responsibilities,” he said.