Greece's left-wing Prime Minister Alexis Tsipras, whose Syriza party has suffered a major blow at the European polls, has said he will ask the country's president to call early elections.

With a third of the ballots counted, Tsipras' Syriza is trailing some 10 percent behind its main rival, the conservative New Democracy Party. According to the preliminary results, Syriza has won 24 percent of the vote, while the conservatives stand at over 33 percent.

In a televised speech, Tsipras said that the outcome of the elections was far from what he had hoped for, but noted that it won't discourage him from political work. "I will not run away or quit the struggle for equality, solidarity, social justice," he said.

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New Democracy leader Kyriakos Mitsotakis has been celebrating the conservatives' strong performance at the polls. In his victory speech, he said that by voting down Syriza, Greeks have "sent a strong message" that they have no more confidence in the socialists' ability to run the country.

"The political change demanded by the citizens has already begun," Mitsotakis said.

Syriza has not only lost ground in the European vote, but also in the local elections that gave New Democracy control over most of the country's regions. The conservative candidates emerged as frontrunners in the mayoral races in the capital Athens and in Thessaloniki, where run-offs will be held.

Tsipras came to power in Greece in January 2015 on the back of a promise to fight harsh austerity measures imposed on his country by the EU. However, he soon reneged on his initial pledge and struck an agreement with international creditors, arguing that it was a life-and-death decision for a country plagued by a severe economic crisis. Tsipras prevented Greece's exit from the eurozone, but drew criticism for not standing up to the EU powerhouses.

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Despite the fact that the economy has been gradually rebounding under Tsipras, and is projected to grow by 2.2 percent this year, the recovery was not enough to sway the voters as a third of the county's population still live in poverty or at an imminent risk of falling into it.

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