ATHENS - Greek leftist Alexis Tsipras stormed back into office with an unexpectedly decisive election victory on Sunday, claiming a clear mandate to steer Greece's battered economy to recovery.

The vote ensured Europe's most outspoken leftist leader would remain Greece's dominant political figure, despite having been abandoned by party radicals last month after he caved in to demands for austerity to win a bailout from the euro zone.

In a victory speech to cheering crowds in a central Athens square, he promised a new phase of stability in a country that has held five general elections in six years, saying his mandate would now see him through a full term.

"Today in Europe, Greece and the Greek people are synonymous with resistance and dignity. This struggle will be continued together for a full four years," he said.

He made no specific reference to the 85 billion euro bailout, but Syriza campaigned on a pledge to implement it, while promising also to introduce measures to protect vulnerable groups from some aspects of the deal.

"We have difficulties ahead of us but we also have a solid ground, we know where we can step, we have a prospect. Recovery from the crisis can't come magically, but it can come through tough work," he said.

Tsipras's first task after forming a government will be to persuade European Union lenders that enough agreed steps have been made to ensure the next payment. The bailout programme is due for a review next month.

Jeroen Dijsselbloem, the Dutch head of the Eurogroup of finance ministers that use the single currency, said he looked forward to the swift formation of a new Greek government with a mandate to implement the bailout.

"Ready to work closely with the Greek authorities and to continue accompanying Greece in its ambitious reform efforts," Dijsselbloem tweeted.

Tsipras will also need to grapple with Greece's central role in Europe's refugee crisis, as the main entry point for tens of thousands of migrants who arrive by sea and trek up the Balkan peninsula to richer EU countries further north. He meets EU colleagues at an emergency summit over the crisis on Wednesday.

In a near repeat of January's general election, his Syriza party fell just shy of an outright majority but will form a coalition with his former partners, the small rightwing Independent Greeks party.

With around 57 percent of votes counted, Syriza was on course to claim 35.5 percent of the vote, easily seeing off the main conservative challengers New Democracy on 28.2 percent.

The interior ministry said that would give Syriza 145 seats in the 300-seat parliament, just four fewer than when Tsipras first stormed to power early this year. The result was more decisive than had been indicated in opinion polls, which had predicted the outcome would be close.

New Democracy swiftly conceded defeat. Leader Vangelis Meimarakis said: "The electoral result appears to be concluding with Syriza and Mr Tspiras in the lead. I congratulate him and urge him to create the government which is needed."

Third place in the election looked set to go again to Golden Dawn, a far right party with a swastika-like symbol, with around 7 percent of the vote.