* First attempt at forming Greek coalition fails
* Markets fret about risk of Greek euro exit
* Merkel tells French president-elect "no renegotiation"
* Hollande seeks to augment fiscal pact with growth plan
* IMF shows new flexibility on fiscal austerity
By Lefteris Papadimas and Paul Taylor
ATHENS/PARIS, May 7 (Reuters) - An anti-austerity backlash by voters in Greece and France shook the euro zone on Monday, causing jitters for the euro currency and stock markets amid deepening doubts about whether Greece has a future in the single currency.
Greece, where Europe's sovereign debt crisis began in 2009, slid into turmoil after an election on Sunday boosted left and right-wing fringe parties, stripping the two mainstream parties that backed a painful EU/IMF bailout of their parliamentary majority.
Uncertainty over whether the country could avert bankruptcy and stay in the euro deepened on Monday when Antonis Samaras, leader of the conservative New Democracy party which won the biggest share of the vote, failed within hours to cobble together a government.
Samaras had had three days to form a coalition. However, his call for a national unity government to keep Greece in the euro zone but renegotiate the bailout programme fell on deaf ears.
Rebuffed by a string of anti-bailout parties, Samaras admitted defeat shortly after President Karolos Papoulias had given him the mandate to negotiate a coalition.
"It was impossible," he told reporters. "I handed back the mandate." Next in line to try to form a government will be Left Coalition leader Alexis Tsipras, whose party came second on a platform of rejecting the austerity conditions of Greece's latest bailout programme.
However, European Commission spokesman Amadeu Altafaj said: "Full and timely implementation of the programme is of the essence in order to meet the targets and (reach) sustainability of the Greek debt."
The Greek result overshadowed France's presidential election, in which Socialist Francois Hollande, who wants to change Europe's policy focus from austerity to restoring growth, ousted conservative incumbent Nicolas Sarkozy.
German Chancellor Angela Merkel, who had openly supported Sarkozy, her partner in euro zone crisis management, promised to welcome Hollande "with open arms" and work with him to maintain strong Franco-German cooperation at the heart of Europe.
But she also made clear there could be no renegotiation of a fiscal discipline treaty. Hollande has said France will not ratify it unless measures are added to promote economic growth.
"We in Germany are of the opinion, and so am I personally, that the fiscal pact is not negotiable. It has been negotiated and has been signed by 25 countries," Merkel told journalists.
"We are in the middle of a debate to which France, of course, under its new president will bring its own emphasis. But we are talking about two sides of the same coin - progress is only achievable via solid finances plus growth," she added.
Jean-Claude Juncker, head of the Eurogroup of euro zone finance ministers, said he had told Hollande on Monday that the European Union's fiscal pact could not be renegotiated.
"It will not be possible to change the substance of the fiscal pact, there will not be a formal new negotiation in that respect," Juncker said after Hollande had telephoned him.
However, he added: "It is possible to add growth elements, not necessarily in the form of a treaty.
Hollande's election gave leaders of struggling southern European countries a new ally in their effort to temper the German drive for austerity that has exacerbated their problems. In a telephone call with Hollande on Sunday night, Italian Prime Minister Mario Monti promised to cooperate on refocusing European policy towards growth.
The International Monetary Fund showed some new flexibility on Monday over how quickly it would press deeply indebted countries to bring their budgets under control if economic growth weakens.
IMF Managing Director Christine Lagarde in a speech in Zurich said the IMF is aware that fiscal austerity holds back growth and the effects are worse in an economic downturn. Hence calibrating the cutbacks and achieving the right pace are essential, she said.
"As next year looms on the horizon, countries need to keep a steady hand on the wheel. If growth is worse than expected, they should stick to announced fiscal measures, rather than announced fiscal targets," she said.
"In other words, they should not fight any fall in tax revenues or rise in spending caused solely because the economy weakens," Lagarde said.
She also said on the world's advanced economies still had to cut their debts or face even more pain.
"The most important element is to lay out a credible medium-term plan to lower debt," she said. "Without such a plan, countries will be forced to make an even bigger adjustment soon."
The Greek and French votes unsettled investors, undermining confidence in Europe's plans to cut spending and tackle the debt crisis, given the scale of public opposition.
The euro fell to a three-month low of $1.2955 in Asia before recovering trade at around $1.3050 at 1830 GMT. European stocks slipped early in the day on the Greek news but most recovered later, except the Athens stock exchange, down 6.67 percent.
French debt was spared from the selloff, in a sign that markets are more relaxed about the moderate Hollande. The yield on French 10-year bonds fell to its lowest in seven months.
In Greece, Sunday's election threatened to produce what daily Ta Nea called a "Nightmare of ungovernability". Among the parties that stormed into parliament were the extreme right-wing Golden Dawn, which won 6.97 percent and 21 seats.
The Left Coalition pushed the former ruling PASOK Socialist party into third place. Between them, New Democracy and PASOK won 149 of the 300 seats, two short of a majority.
Greece had appeared to have averted a disorderly default and euro exit in December when a government led by former central banker Lucas Papademos, and supported by the two main parties, agreed on a second international bailout under which private bondholders accepted sharp write-downs on their holdings.
But the four straight years of recession, wage and pension cuts and still rising mass unemployment drove angry Greeks further to the left and right.
Greece consistently missed targets under its first programme, agreed in April 2010, which led to the restructuring of its private-sector debt under the second package.
Officials say any further backsliding now will not be tolerated, especially with the International Monetary Fund a reluctant partner in the second programme.
Three Greek finance ministry officials told Reuters the country might run out of cash by the end of June if it does not have a government in place to negotiate the next instalment of EU/IMF aid and projected state revenues fall short.
Euro zone leaders have so far done everything to avoid a Greek default and departure from the euro, which Merkel has said would be a catastrophe. Officials are worried by the precedent it could set for other troubled south European countries.
But public support for further bailouts is wearing thin in the euro zone's triple-A rated lenders Germany, the Netherlands and Finland, raising doubts about their willingness to go on supporting a recalcitrant Greece.
Some European diplomats and economists have been predicting the possibility of Greece leaving the euro area for months.
In a research paper published on Feb. 6, Willem Buiter, the chief economist at Citi, raised his estimate of the likelihood of Greece dropping out of the currency zone to 50 percent over the next 18 months, from 25-30 percent previously. On Monday, Citi raised the probability again to 50-75 percent.