* Socialist fails to form unity government
* President to hold final meetings with politicians
* Election likely in mid-June
* Leftist who opposes bailout leads in new poll
By George Georgiopoulos and Renee Maltezou
ATHENS, May 11 (Reuters) - Greece's politicians failed on Friday to agree a new government, sending the country hurtling towards a new vote, with radical leftists leading in the polls and poised to scrap the 130 billion euro bailout that staved off bankruptcy.
The prospect of a new election just weeks after an inconclusive vote that paralysed the most troubled country in the euro zone caused havoc in financial markets.
The European single currency hit its lowest point since January near $1.29, while the Athens stock exchange fell more than 4 percent to its lowest level since 1992.
Outgoing finance minister Evangelos Venizelos, leader of the Socialist PASOK party, acknowledged his failure to form a government after he was spurned by radical leftist Alexis Tsipras, who has sworn to tear up the bailout.
"The moment of truth is here. I will inform the president tomorrow afternoon. I hope everybody shows maturity and responsibility in consultations with the president," he said.
President Karolos Papoulias will now have a last chance to meet with all political leaders to convince them to agree a cabinet, although the odds of success are seen as scant. If he fails as expected, he must call a new election for mid-June.
Venizelos had tried to form a unity coalition government, but the offer was brushed aside by Tsipras, who saw it as a scheme to salvage the bailout that most voters rejected.
"It is not the Left Coalition that has refused this proposal, but the Greek people, who did so with their vote on Sunday," Tsipras said.
Venizelos's PASOK party and its conservative New Democracy partners dominated the country for generations but were punished by voters for jointly agreeing the bailout. Sunday's vote saw their combined share fall to 32 percent from 77 percent.
Still, they had come close to forming a government because of a rule that gives the single largest party - New Democracy - an extra 50 seats in the 300-seat house, an advantage they are now poised to lose.
A new poll showed Tsipras's SYRIZA headed for first place after consolidating the anti-bailout vote, which means he would take the 50 bonus seats and reduce the pro-bailout contingent to only about a third of parliament.
Greek politics would be radically transformed and a thunderbolt felt across Europe, where voters are turning against German-backed austerity, and where the once iron-fast principle that no country could leave the euro currency is now in doubt.
"I appeal to the sense of national responsibility of all (Greek) political leaders to reach an agreement respecting the country's engagement and ensuring its European future," European Council President Herman Van Rompuy said.
The overwhelming majority of Greeks still want to stay in the euro. Tsipras's party says that can be achieved without accepting the terms of the bailout, which was hammered out earlier this year when Greece was weeks away from running out of funds.
"They will be begging us to take the money," SYRIZA deputy Dimitris Stratoulis said of the bailout, arguing that European leaders would not dare risk a Greek exit from the euro that would wreck the single currency project.
But European leaders say they are determined to halt Greek funding if Athens rejects the bailout terms, even if that means pushing it into bankruptcy and a costly exit from the currency.
"We will only give it if Greece meets all agreements. Otherwise they won't get the money," Dutch Prime Minister Mark Rutte said.
TSIPRAS TAPS VOTER FURY
Backers of the bailout say the wage cuts, tax hikes and economic reforms demanded by Brussels are the only way Greece can hope to become solvent. Opponents say it is self-defeating - making Greece's debt problem worse by destroying its chances of economic growth and imposing extreme hardship on a population already enduring five years of recession.
The younger generation has been hit particularly hard - more than half of Greek youth are unemployed. They appear to have found a hero in Tsipras, a boyish 37-year-old civil engineer, ex-Communist and former student leader.
In a country fed up with middle-aged party dynasts widely seen as corrupt, he has become a star - aided by a self-confident manner and good looks.
Samaras and Venizelos may be hoping Greeks - frightened by the prospect of a hasty exit from the euro - will return to their traditional parties in a vote re-run.
But the first opinion poll since the election showed the main beneficiary of a new vote would be Tsipras. It gave SYRIZA 27.7 percent of the vote, almost 11 points up on its Sunday result, and well ahead of New Democracy on about 20 percent.
Ratings agency Fitch said the emergence of a government that disavowed the bailout terms would increase the chance of Greece leaving the euro zone, an event it said would put the credit ratings of all euro countries at risk.
Greece could run out of money as soon as the end of June. The prospect that Greece might declare bankruptcy and leave the euro caused panic across the euro zone last year. Since then, European banks have written off the value of most of their Greek debt, making them less prone to shock if Greece defaults.