SYRIZA party leader Alexis Tsipras has pledged to revive Greece's banks and its crippled economy, while demanding debt relief from creditors in his "first big battle" following an unexpectedly clear election victory that returned him to office as prime minister.

He set the financial priorities at the top of a dauntingly long "to do" list that also includes implementing austerity polices and dealing with waves of migrants landing on Greek shores.

Voters gave Mr Tsipras and his Syriza party a second chance to tackle Greece's problems, and with it the benefit of the doubt over a dramatic summer U-turn, when he ditched his anti-austerity platform to secure a new bailout and avert a Greek exit form the eurozone.

Mr Tsipras has promised to implement the tax increases, spending cuts and market reforms mandated by creditors under the bailout programme, which restrains much of his ability to set policy. But his party says there is still enough flexibility to cushion the impact on the most vulnerable Greeks.

Syriza's stronger-than-expected win secured it 145 of 300 parliamentary seats, meaning the party requires only one small coalition partner to form a government in Greece's notoriously fractious legislature.

It will govern with the same junior party it teamed up with in January, the once stridently anti-bailout right-wing Independent Greeks (ANEL), which won 10 seats. Its leader Panos Kammenos met with Mr Tsipras.

He says his victory gives him a mandate for a full four-year-term, extraordinary in a country that has gone through five general elections in six years.

"This is a major personal triumph for Tsipras," said political commentator Aristides Hatzis. "His political hegemony is (now) unprecedented."