Greece's pro-bailout parties were on course to secure a slim parliamentary majority in Sunday's elections, after an inconclusive general election in May failed to produce a government.

The radical leftists who had vied for first place conceded defeat, after official estimates showed the conservative New Democracy party winning 29.5 percent of the vote, the radical leftist Syriza party receiving 27.1 percent and the PASOK Socialists taking 12.3 percent.

New Democracy leader Antonis Samaras said “the Greek people today voted for Greece to remain on its European path and in the eurozone.”

In Washington, a White House statement congratulated the Greek people on conducting their election in such a difficult time. The statement said “We hope this election will lead quickly to the formation of a new government that can make timely progress on the economic challenges facing the Greek people.” It said that “as President Obama and other world leaders have said, we believe that it is in all our interests for Greece to remain in the euro area while respecting its commitment to reform.”

All of the major parties want the country to stay in the euro. New Democracy has promised to renegotiate the harsh austerity conditions of Greece's bailout by the European Union and International Monetary Fund. But Alexis Tsipras, leader of the Syriza party, called for the annulling of the austerity package altogether, a decision which could have forced Greece to leave Europe's common euro currency.

Samaras said Tsipras' policies will put Greece into a worse situation than it is in now.

The monetary crisis in Greece, which first exploded in 2009, set off a chain reaction across Europe. Greece is now in its fifth year of recession, with unemployment spiraling to above 22 percent. Opinion polls show that Greeks overwhelmingly favor remaining in the euro, but are just as opposed to the austerity drive.