CNN- The men hoping to lead Greece out of the crisis that is threatening Europe's common currency promised their country a bright future on Sunday -- but they have different visions of what that means.
Radical leftist Alexis Tsipras, who hopes to emerge as prime minister, suggested Europe could not push Greece around any more.
"Today we open the path towards a better tomorrow, with our people united, dignified and proud. To a Greece where there's social justice and progress -- an equal member of a Europe that's changing," the leader of the Syriza party said.
His main rival, New Democracy leader Antonis Samaras, said simply: "Today the people of Greece speak. Tomorrow a new era begins for Greece."
They were speaking as Greeks voted in parliamentary elections that will determine who leads a country paralyzed for months by a political and economic crisis.
The party that wins the most seats gets the first chance to form a government.
Syriza was neck-and-neck with New Democracy in the last official polls two weeks ago. No new polls are allowed 14 days before the vote.
The election could decide the fate of the euro, a currency used by 325 million people across 17 countries in Europe.
Yannos Papantoniou, who was the Greek finance minister at the time the country adopted the euro, said the vote was a referendum on being in the common currency.
Support for Syriza --which has soared on the back of Greek anger at government budget cuts imposed by international lenders -- would set up a confrontation with Europe which could lead to a bank run, he said.
Tsipras has vowed to tear up the conditions attached to massive international loans that are keeping Greece from defaulting on its debts.
The possibility that he could emerge as prime minister has 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.
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.
The center-right New Democracy party favors sticking to the terms of the unpopular deal with Greece's lenders, the European Commission, the International Monetary Fund and the European Central Bank. They demanded public spending cuts to slash Greece's enormous deficit.
The radical left-wing Syriza party wants to tear up the current bailout agreement, an act that markets fear will lead to a "disorderly exit" from the eurozone.
Neither party is likely to get a majority on its own, and will need to form a coalition with other parties in order to govern.
Former finance minister Papantoniou, who is now president of the Centre for Progressive Policy Research, said the country needed more flexibility to deal with the austerity measures being demanded by its European lenders.
He said the country needed to implement three changes to its plans to enable it to emerge from the crisis: An extension to the fiscal deficit demands; a commitment to stop lowering incomes and raise taxes; and a European "Marshall Plan" to promote investment and foster growth.
Sunday's election was called after an initial ballot on May 6, the first since Greece's financial crisis exploded, failed to deliver a majority for any one party. Talks to create a government failed.
Since then, Greece -- suffering under a heavy burden of painful austerity measures, high unemployment and a long-running recession -- has been roiled by uncertainty and division.
Many voters were focused on Greece's Euro 2012 soccer match against Russia on Saturday night in Warsaw -- a welcome distraction from the political drama playing out at home, especially after Giorgos Karagounis's goal helped propel the Greek side into the high-profile tournament's quarterfinal round.
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The Greek victory potentially sets them up to play Germany in a future round.
Some analysts fear Sunday's election could again result in no clear winner, leaving Greece with a weak caretaker government at a time when the nation needs clear leadership.
Syriza leader Tsipras has threatened to renege on the terms of Greece's bailout, but he has also expressed a desire to remain in the euro currency union.
Samaras, the leader of New Democracy, has said his party wants to remain in the eurozone and alter existing policies, including stringent austerity measures, to "achieve development and offer people relief."
New Democracy and the Socialist Pasok party were punished by voters in the last election for supporting the bailout program, as well as for agreeing to the austerity measures that came with it.
Pasok party leader Evangelos Venizelos cast his ballot Sunday, calling for a government of shared responsibility.
"We must be united on the home front and have international credibility to be able, with Greece remaining in the Euro, to do what's best for all Greek citizens," he said.
Fotis Kouvelis, leader of the small Democratic Left party and a potential kingmaker if parliament is closely divided, called for progress after hie voted on Sunday, saying the country needed to escape "a situation that cuts us into small pieces and hurts society."
Greece must identify additional budget cuts by the end of June to be considered "compliant" with the terms of its bailout program.
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.
But others worry that such an unprecedented event would cause chaos in financial markets and shock the global economy.