The Independent Greeks were running fourth at 7.5% and 20 seats, while the nationalist, far-right Golden Dawn -- which called illegal immigration the country's biggest issue -- appeared headed for a fifth-place finish at 7% and 18. The Communists brought up the rear at 4.5% and 12 seats, according to Interior Ministry figures.
The Independent Greeks, a conservative nationalist party led by former New Democracy lawmaker Panos Kammenos, saw its support shrink from 33 seats in May to 20, while Golden Dawn -- which hadn't won seats in parliament before -- held steady.
Greece has been suffering under a heavy burden of painful austerity measures, high unemployment and a long-running recession. Syriza and New Democracy were effectively tied in the last official polls two weeks ago, in part because Syriza was seen as offering something new and different, Greek journalist Fanis Papathanasiou said Sunday.
And Yiannis Alafouzos, managing director of Greek broadcaster Skai Media Group, said older Greeks are scared -- "But the younger generation, they're not scared, and they seem to have had enough of the recession they're trying to get out of it by rebelling, effectively."
"Unfortunately, the political system in Greece has not been honest with the voters," Alafouzos said. "And so a lot of people believe there is a way out of this without all the pain we have been suffering for the past two or three years."
The possibility that Tspiras could emerge as prime minister prompted waves of fear that Greece could crash out of the euro and Europe's ambitious experiment with a common currency could collapse. Some analysts have estimated that the collapse of the euro would cost $1 trillion, while others say talk of the break-up of the currency is alarmist and unlikely to happen.
Since May's vote, Greece has been roiled by uncertainty and division, and the country must identify additional budget cuts by the end of June to be considered "compliant" with the terms of its bailout program.
German Chancellor Angela Merkel, Europe's most powerful advocate of balancing budgets to build a strong basis for economic growth, urged Greeks not to walk away from international loan deals.
"We will stick to the agreements. That is the basis on which Europe will prosper," she said Saturday.
But Fotis Kouvelis, leader of the small Democratic Left party and a potential kingmaker in a closely divided parliament, said the country needed to escape "a situation that cuts us into small pieces and hurts society."
The situation in Greece is likely to be on the minds of world leaders as they meet in Mexico on Monday for the Group of 20 summit. Some experts argue that a potential Greek exit would be manageable, assuming the European Central Bank and European Union policymakers respond aggressively, while others worry that the pullout would cause chaos in financial markets and shock the global economy.