Yanis Varoufakis said he was rather seeking direct talks with eurozone leaders, to try to cancel more than half the money Greece owes.
The minister was speaking after meeting Jeroen Dijsselbloem, head of the Eurogroup – the eurozone finance ministers.
Jeroen Dijsselbloem said Greece should stick to its reform commitments.
He said Greece and the Eurogroup had a “mutual interest in the further recovery of the Greek economy inside the eurozone” and warned against Athens acting unilaterally in its efforts to renegotiate its bailout.
Greece has endured tough budget cuts in return for its €240 billion ($270 billion) bailout, agreed in 2010 with the “troika” – the European Commission, International Monetary Fund (IMF) and European Central Bank (ECB).
There was little warmth between the two men at the news conference, with Jeroen Dijsselbloem making a brusque exit.
Breaking with tradition, Yanis Varoufakis wore an open-neck shirt – hanging loose at his belt. Jeroen Dijsselbloem was dressed conventionally.
On the troika, Yanis Varoufakis said: “We have no intention of co-operating with a three-member committee whose goal is to implement a program whose logic we consider anti-European.”
Jeroen Dijsselbloem, who is also Dutch Finance Minister, said the two sides would decide what would happen next before the bailout program ends – that is, by February 28.
He also met Greek PM Alexis Tsipras in Athens, who led the Syriza radical left-wing coalition to victory in elections on Sunday.
Yanis Varoufakis, meanwhile, said Greece was not asking for an extension of the existing bailout, but seeking a “new agreement that will emerge following talks between all Europeans”.
He said he would he seek “maximum co-operation” with Greece’s international creditors, but that he would not work through the “troika”, which he called “a committee built on rotten foundations”.
Jeroen Dijsselbloem rejected Alexis Tsipras’s idea of convening a European conference on debt.
“This conference already exists and it’s called the Eurogroup,” he told the news conference.
Syriza won on an anti-austerity platform, promising to have half of Greece’s debt written off, and to roll back on deep cuts to jobs, pay and pensions.
Greece’s economy has shrunk drastically since the 2008 global financial crisis, and high unemployment has thrown many Greeks into poverty.
The new government has already pressed ahead with cancelling major privatization projects, including of the two main ports of Piraeus and Thessaloniki.
But EU officials have warned there is little appetite among eurozone countries for cutting the debt.
Greece has about €20 billion ($22.5 billion) to repay this year, according to the Greek finance ministry.
Economists estimate that Greece needs to raise about €4.3 billion in the first quarter.
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