What's next for ailing Greece after the latest vote?

Editor's note: CNN's Richard Quest and John Defterios are covering Greece's pivotal election from Athens. Here they analyse what the result means.

Athens (CNN) -- Greece has been at the heart of the European debt crisis -- and its weekend election was a critical test of the 17-country eurozone's ability to retain its common currency.

The pro-bailout New Democracy party narrowly won most votes and claimed "a victory for all Europe," while the anti-austerity left-wing party Syriza a close second; the socialist Pasok party, which held power until late last year, came third.

The results could yet change the course of the continent-wide bloc, as Quest and Defterios explain.

Richard Quest: This result gives New Democracy two options: They can rule as a minority government with agreement from Pasok and Syriza not to bring them down; or they can form a coalition with Pasok.

But Pasok has said it will not join a government without Syriza, which puts a wrinkle in that plan.

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One way or another, there will be no third election. There is no will in the country or in the parties for a third election. But the markets will discount this result quite quickly, whichever way it goes, because of the fragility of the situation. There will be a relief rally that will evaporate over the next six weeks, because of Syriza's support.

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This result has not altered the fundamental problems of the country one jot. Greece is still uncompetitive in the euro. But this result makes it less likely they will leave the common currency.

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Already, Europe's leaders are building bridges, saying they will work with the new government. The European Commission president, Jose Manuel Barroso, and European Council President, Herman van Rompuy, have shown their support in a joint statement, saying they salute the courage and resilience of the Greek citizens.

In this situation, New Democracy's bargaining power is strong because Europe is desperate. I would fully expect the new government to seek to change the terms of the bailout and it will be agreed.

John Defterios: New Democracy's Antonis Samaras did slightly better than expected. There was a perceived 30% threshold for him in this race, with some suggestions that he may have to step aside as leader of a new government if he fails to reach this level.

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At this level he has two distinct options: He either tries to go ahead with a minority government and secure an agreement that there will be no resistance from Pasok and Syriza and the radical left to his revitalization plan to parliament; or move quickly to form a coalition with Pasok and the Democratic Left. The latter would provide more confidence since it would send a message of unity, with discussions likely to have been held on this well before the election. It would also be the preferred option of the international markets.

But there is a lot of tension between the players.

Let's not forget Samaras is the person who pushed out Greece's then-prime minister George Papandreou last year. Pasok leader Evangelos Venizelos was trying to negotiate a broad caretaker government to allow Lucas Papademos, former ECB vice-president, to carry on for at least nine months, or a year, and Samaras resisted that effort. He wanted the elections we saw in May, which were inconclusive and led to this second round.

So we can be sure that there will be a great deal of horse trading going on for different ministerial seats, and different priorities in terms of the austerity program going forward.

This is a country with its back against the wall. Its economy contracted 6.5% in the first quarter of this year and it has sky-high unemployment. Around 22% of the workforce is unemployed and one in two youths are without a job right now.

It is also interesting to note this was a very divided campaign.

New Democracy appealed to those over 50 years old, with a margin of 15%. But Syriza collected the youth vote. Syriza also did very well in major cities like Athens, while Samaras did well in the countryside, where voters are more conservative and he is trusted by the older generation.

So the country remains polarized. The next 24 to 72 hours are going to determine how the international markets see this second round of elections in Greece.

This is a critical window ahead of an EU summit at the end of the month -- and Greece is in need of the bailout funds. Hospitals are running short of supplies, imported natural gas payments need to be made and confidence among Greeks has to be restored, so that they stop pulling money out of the country or stuffing it under their mattresses.

CNN's Irene Chapple contributed to this report