But financial markets' relief that the 17-nation European currency area had avoided plunging deeper into crisis was mitigated by concern about unresolved problems in Greece, the lack of a comprehensive plan for the euro zone as a whole and weakness in the world economy.
German Foreign Minister Guido Westerwelle said the substance of Greece's austerity and economic reform program, agreed in exchange for a second EU/IMF rescue, was non-negotiable, but the timing could be adjusted.
"We're ready to talk about the timeframe as we can't ignore the lost weeks and we don't want people to suffer because of that," Westerwelle said in a radio interview.
Government officials said his comments did not reflect Berlin's official position, and a government spokesman said now was not the time to give Greece "a discount".
However, Deputy Finance Minister Steffen Kampeter, who is closer to Chancellor Angela Merkel and normally a stickler for strict adherence to fiscal orthodoxy, told ARD television: "It is clear to us that Greece should not be over-strained."
Austrian Chancellor Werner Faymann said Greece needed both a sustainable course of fiscal consolidation and a return to economic growth after four years of crippling recession.
"The conditions that were negotiated have to be observed but we also need to give the Greeks room to breathe," Faymann said in a statement. "For example it must be assured that people have sufficient access to medicine. Consolidation cannot be carried out solely on the backs of the people."
The hints at leniency should help Greek conservative leader Antonis Samaras, whose New Democracy party narrowly outpolled the radical leftist anti-austerity SYRIZA movement in Sunday's election, to form a mainstream coalition with the centre-left Pasok Socialists.
He will face fierce pressure from European and International Monetary Fund lenders to start implementing seriously an economic reform program agreed earlier this year, which has largely remained a dead letter so far.
With trust in Greek politicians at a low ebb, a senior EU official said the new government would find a 100-day action plan on its desk including privatizations, axing public sector jobs and closing loss-making enterprises to prove it was serious.
"There will be a very clear 100-day plan for a new government. If it's not implemented in full then the game is over," the German EU official told Reuters before the election.
Procedurally, the next step after the formation of a government will be for the "troika" of European Commission, IMF and European Central Bank inspectors to return to Athens to review Greek implementation of the bailout agreement.
The euro and shares rallied briefly after the Greek vote, but there was no let-up for the borrowing costs of euro zone strugglers Spain and Italy.
Italian Prime Minister Mario Monti welcomed the Greek election result, telling reporters in Mexico on arriving for a G20 summit: "This allows us to have a more serene vision for the future of the European Union and for the euro zone."
Spanish Prime Minister Mariano Rajoy called the outcome "good news for Greece, very good news for the European Union, for the euro and also for Spain".
But Spanish and Italian 10-year government bond yields rose, with Spain's hitting a fresh euro era record above 7.1 percent, close to levels that drove Greece, Ireland and Portugal to seek international rescues.
Analysts at Citi said the election had changed nothing fundamental and they still forecast a 50 to 75 percent likelihood of Greece leaving the euro within 12 to 18 months.
Others said that regardless of whether Greece stays or goes, the key issues driving markets are whether the world's central banks will do more to revive global growth, and whether euro zone leaders can sketch out a roadmap for closer fiscal and banking union at a summit next week to convince investors that the euro will survive.
"It remains vital that eurozone governments take profound steps forward in terms of fiscal union and restoring confidence in the banking sector," said Nick Kounis of Dutch bank ABN AMRO.
"Judging by past form, European politicians tend to take their foot off the gas when the pressure is off."
AUSTERITY ISN'T WORKING
Samaras has pledged to renegotiate key elements of the 130 billion euro ($165 billion) bailout program to soften the economic impact.
Giving Athens an additional year to achieve its deficit reduction goals would mean increasing the size of the euro zone's bailout, raising the commitment by countries such as Germany, the Netherlands and Finland where voters are deeply reluctant to approve further funding.
Greece is in the fifth year of a crippling recession that has driven unemployment to a record 22 percent - including one in two young people - and caused widespread hardship.
Although sufficient voters cast their ballots out of fear of a disastrous euro exit to give mainstream parties a working majority, a majority of electors angry over austerity and corruption voted for a range of anti-bailout fringe groups.
That raises the prospect of a renewal of violent street protests if a Samaras-led administration moves ahead with the unpopular cuts and closures demanded by international lenders.
There is little sign so far that austerity is working in Greece. Public wage, pension and spending cuts have exacerbated economic contraction, shrinking revenue needed to service the debt mountain, while bureaucracy, corruption and a lack of confidence have held back private sector investment.
Many citizens in a fractured society have responded by sullenly refusing to pay bills and taxes out of disgust with their political leaders and fury at seeing the rich evading tax and parking money abroad.
Even if the economy began to recover, economists argue the demands being made of Greece to reduce its public debt to a sustainable trajectory are unrealistic.
If, as expected, the "troika" finds that Greece is off course, pressure among non-European states for the IMF to pull out of the program is bound to rise, diplomats said. The euro zone may end up carrying the whole cost of the bailout, which in turn could fuel public opposition in northern European creditor countries, they said.
(Additional reporting by Jeremy Gaunt and Alan Wheatley in London, Jan Strupczewski and Philip Blenkinsop in Brussels, Lisa Jucca in Milan, Paul Day in Madrid; Writing by Paul Taylor; editing by Janet McBride)