By Nektaria Stamouli 

ATHENS--Greeks headed to the polling booths Sunday for the third time in less than three years to elect a new government, a vote that could determine the country's future in the eurozone and reverberate across Europe.

According to recent public-opinion polls, Greece's radical leftist Syriza party was poised to win the general elections, but it wasn't clear whether its share of the vote would be enough to clinch an outright majority in the legislature.

Syriza has been steadily leading in the opinion polls for the past year, while its lead has widened further in the days immediately before Sunday's vote. The polls show the party garnering between 29.6% and 33.4% of the vote, edging out the incumbent New Democracy party by five to 10 percentage points.

The outcome could have lasting repercussions for both Greece and the eurozone. Syriza, which emerged as the main opposition party in mid-2012 at the depths of the nation's debt crisis, has promised to tear up the austerity and overhaul program that Athens pledged in exchange for a EUR240 billion ($269 billion) bailout from international creditors.

Since that deal, Greece has undertaken a broad sweep of revamps and cutbacks that have helped fix its public finances and nudged the economy back to growth following six years of deep recession. Those cutbacks have come at a cost: Some 25% of Greeks remain jobless, while a quarter of households live close to the poverty line.

However, Syriza's promises to roll back many of those overhauls and its demands for debt relief from Greece's international creditors have also stoked fears of an open clash with eurozone partners that could lead to the country's exit from the common currency and once again rattle financial markets world-wide. In the past three months, Greece's financial markets have shed roughly a fifth of their value, while nervous depositors have withdrawn several billions of euros from the country's banking system.

A Syriza victory would also be closely watched by other antiausterity parties in Europe--on the left and the right---that have been gaining ground in the past year.

Under Greece's electoral law, the winning party is awarded 50 bonus seats in the country's 300-member Parliament, a measure aimed at facilitating the stability of an elected government. But even with that bonus, Syriza doesn't look as if it will have enough seats to form a government on its own. Polls show it might fall two to five seats short and would need to turn to another party to help govern, putting the third-place finisher in a position to become a kingmaker.

The favorite to take third is To Potami, a middle-of-the-road party launched by a prominent television journalist in March that has rapidly drawn voters disillusioned with Greece's traditional political parties. It is running neck-and-neck for third place with the ultranationalist Golden Dawn in the polls, at between 5% and 7%.

To Potami's leader has been coy about whether he would agree to form a coalition with Syriza, saying he would prefer some kind of national unity government of the top parties.

Another possible ally for Syriza is Independent Greeks, a right-wing party that has little in common with the leftists apart from the antiausterity stance, but it wasn't clear whether the party would manage to cross the necessary threshold to enter Parliament.

Write to Nektaria Stamouli at nektaria.stamouli@wsj.com