The narrow election victory of Greece's pro-bailout New Democracy party has been welcomed by world leaders, who urged Athens to quickly form a cabinet.
The eurozone group said reforms were Athens' "best guarantee" to overcome tough economic and social challenges.
The US stressed that it was in everyone's interests "for Greece to remain in the euro area".
The the anti-bailout Syriza party, which came a close second, said it would lead the opposition.
With more than 99% of votes counted, interior ministry results put New Democracy on 29.7% of the vote (129 seats), Syriza on 26.9% (71) and the socialist Pasok on 12.3% (33).
Greek voters went to the polls on Sunday after following May's inconclusive elections.
Speaking after the voting ended, New Democracy leader Antonis Samaras said Greeks had chosen to stay in the euro, and called for a "national salvation government".
Syriza's leader Alexis Tsipras agreed that Mr Samaras should be first to try to form a coalition.
Mr Tsipras stressed that the party would not take part in the government, and would instead become a powerful anti-austerity voice in the opposition.
The vote was watched around the world, amid fears that a Greek exit from the euro could spread contagion to other eurozone members and deepen the turmoil in the global economy.
Tough austerity measures were attached to the two international bailouts awarded to Greece, an initial package worth 110bn euros (£89bn; $138bn) in 2010, then a follow-up last year worth 130bn euros.
Stock markets responded positively to Sunday's results, with share prices up in Asian trading.
'No more adventures'
In a statement on behalf of the 17 eurozone finance ministers, Luxembourg Prime Minister Jean-Paul Juncker said that "continued fiscal and structural reforms are Greece's best guarantee to overcome the current economic and social challenges and for a more prosperous future of Greece in the euro area".
Mr Juncker stressed that "the eurogroup reiterates its commitment to assist Greece in its adjustment effort in order to address the many challenges the economy is facing".
The statement said that the ministers now expected representatives of the European Commission, the European Central Bank and the International Monetary Fund - the so-called Troika - to return to Athens as soon as there was a Greek government in place.
In Berlin, German Finance Minister Wolfgang Schauble said that the election result was "a decision by Greek voters to force ahead with the implementation of far-reaching economic and fiscal reforms".
However, Mr Schauble warned that "this path will be neither short nor easy but is necessary and will give the Greek people the prospect of a better future".
After initial results suggested his narrow victory, Mr Samaras said that "the Greek people voted today to stay on the European course and remain in the eurozone".
"There will be no more adventures. Greece's place in Europe will not be put in doubt," he added, promising that Athens would "honour its obligations".
The BBC's Mark Lowen in Athens says that suggests Mr Samaras wants to press ahead with spending cuts demanded by the country's international creditors.
European leaders have warned that if a new Greek government rejected the bailout, the country could be forced to abandon the single currency.
While the radical-left Syriza and other smaller parties have opposed the bailout, New Democracy and Pasok said they would keep it in a renegotiated form.
New Democracy should be able to build a majority coalition with the socialist Pasok, benefiting from a rule which gives the leading party 50 extra seats in the 300-seat chamber.
However, coalition talks may not be easy. After a first, inconclusive election six weeks ago, each of the main parties tried but failed to form a coalition government.
The leader of Pasok, Evangelos Venizelos, proposed a broad four-party coalition including New Democracy, Pasok, the Democratic Left and Syriza.
"No decision can be taken without this national unity," he said.
Analysts suggested Mr Venizelos had doubts over the viability of a coalition with a narrow majority.
When his party was in power it suffered numerous defections and rebellions as it tried to impose unpopular austerity measures.
Our correspondent, Mark Lowen, says that with such a strong showing by Syriza, Greece could be in for an autumn of discontent by opponents of the bailout deal.
Four other anti-bailout parties look set to take between 60 and 70 seats. They include the far-right Golden Dawn, which looked set to secure nearly 7% of the vote.