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(Reuters) - Greek radical leftist leader Alexis Tsipras, running to head the European Commission, said on Thursday his country's EU-led bailout has been a failure, despite Athens' recent return to bond markets.

"What happened in Greece is not a success story but a social tragedy that shouldn't be repeated anywhere in Europe," Tsipras said during a debate among candidates for president of the European Commission, to be appointed after EU Parliament elections May 22-25.

Greece is also holding two rounds of municipal elections on May 18 and on May 25.

Tsipras, the European Left's candidate in the European elections, made his first appearance in a string of televised debates among the contenders. These debates are the first of their kind as the EU seeks to show its relevance to increasingly hostile voters.

The other candidates to run the EU's executive are centre-right Luxembourg politician Jean-Claude Juncker, 61-year old Belgian liberal Guy Verhofstadt, 32-year old Green politician Ska Keller from Germany and German Socialist Martin Schulz, 58.

Tsipras reiterated demands for Europe-wide debt reduction and called for an end to bailout-imposed austerity policies across Europe to boost economic growth.

"If we don't finish with austerity, we'll never solve the problem of unemployment," said the Athens-trained civil engineer, the only debate participant to speak in his native language.

Juncker, 59, who led Greek rescue talks as head of euro zone finance ministers four years ago, dismissed Tsipras' criticism. "I did what I could to make Greece stay in the euro. I will never accept the charge that we lacked in solidarity," he said.

Tsipras, 39, stands little chance of becoming Commission president. But he expects the candidacy to boost his radical leftist Syriza party, which stunned the political establishment in 2012, coming out of nowhere to become Greece's second-biggest party and the main parliamentary opposition.

Syriza has since staunchly opposed the terms of Greece's 237 billion euro bailout, which saved the country from bankruptcy at the price of severe austerity and record unemployment.

The outcome of the European elections in Greece is being closely watched by financial markets for any sign of growing political risk in the country, which remains dependent on aid from the EU and IMF despite its successful bond sale last month.

Greece's pro-bailout government says it will need no further rescue when the current one expires later this year.

Tsipras has said he would seek to negotiate an international write-off of about one-third of Greece's debt if Syriza came to power but said he prefers a consensus solution rather than using the option of a Greek default as a weapon.

Tsipras has recently moderated some of his more aggressive rhetoric and sought to position himself as a pro-Europe politician.

Again in contrast with his rivals, Tsipras opposed EU sanctions against Russia over the Ukraine crisis.

Syriza has led in the polls in the run-up to the local and EU vote in Greece, but Tsipras has failed to open a wide lead over Prime Minister Antonis Samaras's New Democracy party.

(Reporting by Harry Papachristou; Editing by Cynthia Osterman)