By Renee Maltezou

ATHENS (Reuters) - Greek Socialists elected Finance Minister Evangelos Venizelos as their leader on Sunday, with a mandate to revive a party weakened by unpopular austerity policies ahead of parliamentary polls expected by early May.

Venizelos, who has spearheaded the country's marathon debt talks, is set to resign from his post this week to focus on the general election, with all surveys showing the PASOK socialists badly trailing the conservative New Democracy party.

Tens of thousands of PASOK supporters flocked to polling stations across the country on Sunday to cast a vote for Venizelos, 55, who ran unopposed in the leadership race after winning the backing of all the party's heavy hitters.

"People sent a strong message that PASOK is here, that PASOK hasn't lost its soul, that our target to win the (general) election is feasible," Venizelos told party members. "We will move forward together."

Venizelos, a constitutional law expert turned politician and known for his sharp rhetoric, took PASOK's helm from former prime minister George Papandreou, who stepped down after becoming increasingly unpopular over tax hikes and wage cuts imposed to fight the country's worst crisis in decades.

The debt-choked country averted an uncontrolled default earlier this month when it struck a debt exchange deal with private creditors that paved the way for the EU and IMF to approve a 130-billion euro bailout.

Completion of the second EU/IMF aid package will mean the end of the coalition government under technocrat Prime Minister Lucas Papademos, which was formed in November with a mandate to conclude the bailout and then hold elections.

Both parties backing the coalition government, PASOK and New Democracy, have seen their popularity sink in the run-up to the election which is unlikely to produce an outright winner as small, left-wing, anti-austerity parties gain at their expense.

Regardless of who wins the general election, Germany and international lenders have warned Greece it must keep its promises to keep getting the aid it needs to stay afloat.

Venizelos, the son of a provincial lawyer from Greece's second city Thessaloniki, was first elected to parliament in 1993. He went on to hold a series of ministries including justice and defense. As culture minister, he was in charge of preparing the successful 2004 Olympics in Athens.

In 2007, Venizelos lost a battle for the PASOK party leadership to Papandreou, mainly because he came across as too ambitious, analysts say. But supporters say he has grown wiser after taking on the task of tackling Greece's fiscal woes.

"I voted for him because he gives me hope," said 69-year-old pensioner Dimitra Adrakta after casting her vote in Athens. "I believe he can get us out of the crisis."

The exact date of the general election has not been fixed, but it is expected to be held at the end of April or early May.

(Editing by Ingrid Melander and Karolina Tagaris)