"Today the Greek people expressed the will to stay anchored within the euro, remain in the eurozone and foster growth," New Democracy leader Antonis Samaras said.
The outcome was welcomed by U.S. administration.
"We congratulate the Greek people on conducting their election in this difficult time," a statement issued by the White House press secretary's office 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. 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. Going forward, we will engage Greece in the spirit of partnership that has guided our alliance and the friendship between our people.'
The Greek newspaper Ekathimerini reported that with 60 percent of the votes counted, New Democracy had 30.14 percent of the vote to 26.46 for Syriza, 12.57 percent for the Pasok Party, 7.43 percent for the Independent Greeks, 6.95 percent for Golden Dawn, 6.06 percent for Democratic Left and 4.5 percent for the Communist Party.
Other parties, including the Ecologist Greens, came in below the 3 percent threshold needed for them to win representation in Parliament.
The results mean New Democracy would garner 130 seats in the 300-seat Parliament to 70 for Syriza, 33 for Pasok, 20 for Independent Greeks, 19 for Golden Dawn, 16 for Democratic Left and 12 for the Communist Party, the newspaper said.
Samaras urged the various factions "to join a government of national salvation," Ekathimerini said.
"There is no time for political games, the country must be governed," he said.
But Alexis Tsipras, leader of the radical-left Syriza Party, made it clear his party would not be party of a coalition with New Democracy and would not try to form government if New Democracy fails in its attempt.
"We will be present in developments from the position of the main opposition party," Tsipras said. "We have opposite us an unholy alliance of yesterday's powers, from inside and outside the country.
"Our proposals for rejection of the memorandum are the only viable solution not only for Greece but also for all Europe."
The Syriza Party had campaigned to keep the euro currency but to ease austerity in debt-laden Greece as part of the terms for the financial bailout by the European Commission, International Monetary Fund and the European Central Bank.
Greece last held parliamentary elections May 6 and no party won enough seats to form a government outright and efforts to form a ruling coalition failed.
Apart from national bankruptcy, the specter of Greece abandoning the 17-country euro currency and returning to the drachma has raised international financial concerns.