Greek leftists rejected a last-ditch proposal by the head of state on Monday to put technocrats in charge of the country, as financial markets slid on ever-stronger fears of a Greek euro exit.

President Karolos Papoulias has summoned party leaders to hear his proposal on Tuesday, Reuters reported. They agreed to attend but expressed little hope it would resolve a deadlock which has left Greece with no government to steer it away from bankruptcy.

If Papoulias's proposal fails, he must call a new vote, which opinion polls suggest would be won by leftist opponents of a painful EU/IMF bailout. European leaders say that unless Greece fulfills its bailout commitments, they will cut off funding, which could push Greece out of the euro.

The disarray stems from the election on May 6 that left parliament split evenly between supporters and opponents of the 130 billion-euro ($168-billion) bailout deal. Neither side, each including several parties, has been able to form a government.

Papoulias will present his proposal to party leaders at 2 p.m. (7 a.m. ET) on Tuesday, but the bailout's most influential opponents - the radical leftist Syriza party which was a big winner in the election - said it saw it as just another way to foist on Greece a government that would implement the sharp cuts in spending and the tax increases demanded by the bailout plan.

We will attend the meeting. But we are sticking to our position. We don't want to consent to any kind of bailout policies, even if they are implemented by non-political personalities, Syriza spokesman Panos Skourletis said.

The fact that it's going to be implemented by non-political people doesn't change the purpose of this government, which is to implement the bailout.

Papoulias resolved a similar deadlock six months ago by naming technocratic former central bank governor Lucas Papademos as prime minister, a move that allowed the bailout negotiations to be concluded. But this time, the anti-bailout contingent in parliament is stronger and angrier.

Still, there was considerable speculation Monday night that a technocratic administration might emerge from the meeting, the Irish Times reported.

We may see the formation of an extra-parliamentary government, enjoying the confidence of Pasok, New Democracy, the Democratic Left and, possibly, some individual MPs, said analyst Ilias Nikolakopoulos. The cabinet would be comprised mainly of technocrats, with limited participation by elected politicians. 

Syriza leader Alexis Tsipras called for a meeting of all political leaders, with the exception of the head of the neo-Nazi Golden Dawn party.

In a desperate attempt to stave off fresh elections, which could be held as early as June 17, the three leaders at Monday night's meeting appeared to adopt Tsipras's proposal.

Many have questioned the point of inviting the remaining two parties to the negotiating table as one, the orthodox Communist Party (KKE), flatly rejects all coalition scenarios, while the other, the Independent Greeks party, has said that it would only participate in a coalition that rejected the terms of the bailout memorandum.

The decision to exclude Golden Dawn, which has 21 MPs in parliament, from any further talks on forming a government came after comments made by its leader, Nikos Michaloliakos. He said that, while there were crimes committed in Nazi concentration camps, there were no ovens, this is a lie, before adding that there were no gas chambers either. 

The prospect that a new vote would bring Syriza and its allies to power - accompanied by open threats by European Union leaders to eject Greece from the euro if it abandons the bailout - sent European shares sliding and Spanish and Italian bond yields higher. Investors fear a Greek exit could make it harder for Madrid and Rome to persuade creditors to keep lending.

Socialist leader Evangelos Venizelos, whose party commanded a majority in the outgoing parliament but was reduced to third place in last week's electoral earthquake, backed Papoulias's proposal. But he doubted it would succeed.

We support a government of personalities as an emergency solution, he said. It's not normal to have a government by technocrats or personalities but when you are in such a crisis, in such a dead end, we have to accept this as well.

He added: Things are very difficult. I'm not optimistic.

Venizelos said Pasok would do everything possible to form a national unity government, but it was ready for new elections if necessary, CNN reported.

The Communist KKE party, meanwhile, called for new elections, saying it will not participate in a coalition government.

The gravity of the situation was underscored Sunday by Tsipras, who told leaders, I am concerned that if we carry on with implementation of the bailout conditions in Greece, then Greece is at risk of facing a humanitarian crisis.

His remarks were made in a private meeting, a transcript of which was released Monday.

The leader of the moderate Democratic Left party, which has enough seats to offer the pro-bailout parties a majority but has refused to join a coalition without Syriza, said he opposed the technocrat proposal as well.

I told the president that a government by technocrats or personalities would suggest the failure of politics, and raised my objection, Fotis Kouvelis said.

With Greece set to run out of money as early as next month and no government in place to negotiate the next aid tranche, investors are now betting that a long-speculated Greek default and euro exit will happen sooner rather than later.

There's a real risk for the market that at some point Greece will have to leave the euro if they don't find political cohesion, said ING strategist Alessandro Giansanti.

Emboldened by a reinforced financial firewall to protect weak euro zone states, and by an injection of cheap money to banks from the European Central Bank, EU leaders have broken a taboo by openly discussing the possibility of Greece leaving the currency zone, stressing it is a choice for Greeks to make.

We wish Greece will remain in the euro and we hope Greece will remain in the euro ... but it must respect its commitments, European Commission spokeswoman Pia Ahrenkilde Hansen told a regular news briefing in Brussels, responding to a question she would have probably avoided just weeks ago.

Greece has its future in its own hands and it is really up to Greece to see what the response should be.

German Chancellor Angela Merkel, leader of the continent's biggest and strongest economy, said it would be better for Greece to keep the euro and EU leaders should help it recover. But she added that such solidarity would cease in what she called the unlikely event of Athens reneging on agreements.

The prospect of national bankruptcy and a return to the drachma appeared to be slowly sinking in among Greeks, who must now choose between the pain of spending cuts demanded in return for aid and the prospect of even more hardship without the euro.

We have to stay in the euro. I've lived the poverty of the drachma and don't want to go back. Never! God help us, said Maria Kampitsi, 70-year old pensioner, who was forced to shut her pharmacy two years ago due to the economic crisis.

They must cooperate or we'll be destroyed, she said of the squabbling politicians. It will be chaos.

Capturing the desperate mood, the Ta Nea daily ran a front-page image of a man in silhouette shooting himself in the head and red blood spattering behind to form a map of Greece.

Syriza has paved the way for new elections. And this time, whether we like or not, they will be more like a referendum. We will have set ourselves the question whether we prefer the euro or the drachma, centre-left daily Ethnos wrote in an editorial.

Polls show the divided anti-bailout vote has consolidated this week around Syriza, now on course to place first in a new vote, a prize that brings a bonus of 50 extra seats in the 300-seat parliament at the expense of pro-bailout conservatives.

European leaders in recent days have reacted with growing disbelief to the rhetoric from Tsipras, who has promised Greece can simultaneously renege on the terms of its bailout and stay in the euro zone.

The chairman of the euro zone group, Luxembourg Prime Minister Jean-Claude Juncker said he was strongly against a Greek exit from the single currency, calling the suggestion nonsense and propaganda, the BBC reported.

But the Greek public, the Greek citizens, have to know that we agreed on a program and this program has to be implemented, Juncker told a news conference in Brussels.

The Dutch finance minister said Greece had no option but to reform, while Austria said Greece would have to leave the EU in order to leave the euro.

Greece would have to reapply and then we would have membership negotiations and look very closely whether Greece would be able to become a member at all, Austrian Finance Minister Maria Fekter said.