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Afrasianet - Anti-austerity Syriza party leader Alexis Tsipras has vowed to end Greece's "five years of humiliation and pain" after his general election win.
Before cheering supporters, Mr Tsipras again pledged to renegotiate Greece's massive international bailout.
With nearly all of the votes counted in Sunday's poll, Syriza looks set to have 149 seats, just two short of an absolute majority.
Syriza's victory has raised fears about Greece's future in the euro.
The governing centre-right New Democracy came a distant second.
Outgoing Prime Minister Antonis Samaras admitted defeat and phoned Mr Tsipras to congratulate him.
Greece has endured tough budget cuts in return for its 2010 bailout, worth €240bn (£179bn; $268bn) and negotiated with the so-called troika - the European Union, International Monetary Fund (IMF) and European Central Bank (ECB).
The economy has shrunk drastically since the 2008 global financial crisis, and increasing unemployment has thrown many Greeks into poverty.
Syriza's election result will send shockwaves through Europe, the BBC's Gavin Hewitt in Athens reports.
A majority of voters in Greece have essentially rejected a core policy for dealing with the eurozone crisis as devised by Brussels and Berlin, our correspondent adds.
The election result is expected to be one of the main issues at Monday's meeting of 19 eurozone finance ministers.
In Germany, Bundesbank President Jens Weidmann said he hoped "the new Greek government will not make promises it cannot keep and the country cannot afford".
Belgian Finance Minister Johan Van Overtveld was quoted by VRT network as saying that Greece "must respect the rules of monetary union", although he added that there was room for some flexibility.
Meanwhile, the euro fell to $1.1098 against the dollar - the lowest level in more than 11 years.
'Catastrophic austerity'
Addressing his cheering supporters in Athens late on Sunday, Mr Tsipras said "the Greeks wrote history".
"Greece is leaving behind catastrophic austerity, it is leaving behind the fear and the autocracy, it is leaving behind five years of humiliation and pain".
"Your mandate is undoubtedly cancelling the bailouts of austerity and destruction.
"The troika for Greece is the thing of the past," he added.
Mr Tsipras promised to write off half of Greece's debt, but was ready to negotiate "a viable solution" and wants the country to stay in the eurozone.

