ATHENS, Greece (AP) — Greece voted Sunday in an early general election that could alter the course of the country's battle against crippling debts, with a radical left party favored to win by promising to rewrite the terms of its international bailout.

The Syriza party led by Alexis Tsipras has remained firmly ahead of conservative Prime Minister Antonis Samaras' New Democracy party in opinion polls throughout the election campaign, which was called two years ahead of schedule.

But those polls also have shown that a significant portion of voters remained undecided until the last minute, and suggest that Syriza might struggle to win enough parliamentary seats to form a government on its own.

"These elections are crucial for our future and for the future of our children," Samaras said after he cast his ballot in a southern Greek town. "Today we decide whether we will go forward with strength, with security, with assuredness, or whether we will head into adventures."

Samaras said he was optimistic of victory given what he called the "unprecedented large number" of undecided voters. He said they would determine the outcome.

Tsipras was mobbed by a media throng as he voted in Athens. "The Left's time has come!" chanted a nearby pack of his party's youth activists.

A relaxed-looking Tsipras joked with journalists jostling for quotes and photos to calm down. "We've been waiting for this moment for five years. You can wait for another five minutes," he said.

"Today, the Greek people are called to decisively make the remaining step toward the return of hope, the end of fear, the return of democracy and dignity in our country," he said outside the polling station. He said a vote for Syriza would ensure that Greece negotiated "a tough bargain to rejoin Europe on an equal basis. I am optimistic this will be a historic day."

Syriza has promised to renegotiate the country's 240 billion euro ($270 billion) international bailout deal. It has pledged to reverse many of the reforms that international creditors demanded in exchange for keeping Greece financially afloat since 2010.

The anti-bailout rhetoric has renewed doubts over Greece's ability to emerge from its financial crisis that has seen a quarter of its economy wiped out, sent unemployment soaring and undermined the euro, the currency shared by 19 European countries.

Greece's creditors insist the country must abide by previous commitments to continue receiving support, and investors and markets alike have been spooked by the anti-bailout rhetoric. Greece could face bankruptcy if a solution is not found, although speculation of a "Grexit" — Greece leaving the euro — and a potential collapse of the currency has been far less fraught than during the last general election in 2012.

Samaras' campaign focused on the improving economy, which grew for the first time in six years in the third quarter of 2014. He has promised to reduce taxes if re-elected and has warned of the potentially dire consequences of reneging on bailout conditions. Opponents accused him of using fear tactics.

Syriza's promises to end Greece's era of crushing austerity have attracted many voters infuriated by the deterioration in their standard of living and ever-increasing tax bills.

The big question is whether any party will win the required 151 seats in the 300-member parliament to form a government on its own. The Greek political scene has fractured during the financial crisis, with voters abandoning the two formerly dominant parties — the conservatives and the socialists — in favor of a smattering of smaller parties.

Samaras' coalition partner, socialist leader and Deputy Prime Minister Evangelos Venizelos, said he hoped voters "will make choices that will lead them to something better."

But polls indicated his party could continue its precipitous fall since it signed Greece's first bailout aid deal in 2010. The socialists, which have governed alongside the conservatives since November 2011, have seen their vote collapse from 44 percent in 2009 to barely 12 percent in 2012. Polls suggest they may struggle to win 5 percent of votes Sunday.

Challenging the socialists for third place are a new centrist party called To Potami (The River) and the Nazi-inspired Golden Dawn, whose leader and several top lawmakers are in jail awaiting trial on charges of participating in a criminal organization.

Potami leader Stavros Theodorakis said his party wanted to help the next government steer Greece "in the right direction" while avoiding conflict with EU partners. "Let's change everything without ruining the country," he said.

Mara Ramou, an official at one Athens polling center, said she hoped the vote would produce a stable government without the need for a second contest, as happened in 2012.

"I hope the votes will express what people truly want and believe, so that things change for us," she said, adding her concern that social and financial pressures would not "get worse in Greece than what they already are, because austerity and the crisis touch all levels of society."

Without the required 151 seats, whichever party wins the most seats will have to try forming a coalition government with at least one other party. The first three parties each have three days to try and form a coalition government to avoid a second election being called within a month.

Another option would be for the winner to form a minority government. This would require at least one other party to support the government in parliament without taking part in a formal coalition.

Greece's next government faces a series of formidable tasks, the most pressing of which is concluding negotiations with bailout inspectors to release a 7.2 billion euro ($8.1 billion) loan installment originally due late last year.

The inspectors "must come soon," Finance Minister Gikas Hardouvelis said Saturday.

The new government also must negotiate some kind of relief for Greece's 320 billion euro debt and bolster weak growth.

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Associated Press reporter Demetris Nellas in Athens contributed to this report.