The shock announcement came as European leaders scrambled for a response after Greek voters said a resounding "No" to further austerity measures in return for bailout funds in a referendum that could see the country crash out of the eurozone.
The euro rose after Varoufakis's announcement, which was expected to renew hopes that the creditors - the ECB, the EC and the International Monetary Fund (IMF) - could be persuaded back to the negotiating table despite the country's decisive rejection of the reforms they were demanding in return for the release of a final tranche of bailout funds.
German Chancellor Angela Merkel was to meet with French leader Francois Hollande in Paris amid a flurry of other meetings to size up the implications of the vote, a victory for Greece's radical left-wing Tsipras, who insisted it did not mean a "rupture" with Europe.
European Union president Donald Tusk said an emergency eurozone summit would be held on Tuesday.
With the ramifications still unclear and some analysts putting the chances of a "Grexit" at "very high", European Commission head Jean-Claude Juncker was to hold a teleconference on Monday morning with European Central Bank chief Mario Draghi, Tusk and Eurogroup head Jeroen Dijsselbloem.
Meanwhile German and French finance ministers were set for talks beginning in Warsaw, while the Euro Working Group of top treasury officials will meet in Brussels.
European leaders had reacted with a mix of dismay and caution to the figures released by the Greek interior ministry early Monday showing the final tally in the referendum at 61.31 per cent "No" and 38.69 per cent "Yes", with turnout at 62.5 per cent.
Britain vowed it would do "whatever is necessary" to protect its own economic security in light of the vote.
In Asian trade, the single currency held up against the dollar, after dropping in the immediate wake of the vote.
In a televised address after the referendum, Tsipras insisted the vote did not mean a break with Europe.
He has emphasised that euro membership is meant to be "irreversible", with no legal avenue to boot a country out.
"This is not an mandate of rupture with Europe, but a mandate that bolsters our negotiating strength to achieve a viable deal," he said.
Tsipras said the creditors would now finally have to talk about restructuring the massive, 240-billion-euro ($A357 billion) debt Greece owes them.
Thousands of people in Athens gathered to celebrate the "No" vote Sunday night, punching the air, kissing and cheering.
But the mood of jubilation was not shared by all "No" voters, with some saying they had been confronted with an impossible choice.
Greece is teetering on the brink of financial collapse.
If it does not receive cash and loans soon from European institutions, it could be forced to resort to government IOUs or a return to the drachma to keep its economy running.
Greece was officially declared in default on Friday by the European Financial Stability Facility, which holds 144.6 billion euros of Greek loans.
Greek banks are now reportedly almost illiquid after a run by panicked customers in the lead-up to the referendum, which Tsipras abruptly called on June 27 to break an impasse with the creditors.
A weeklong closure of the banks and capital controls that included restricting daily ATM withdrawals to just 60 euros and blocking money transfers abroad slowed the outflow.
But if the ECB does not inject emergency euros into Greece's banks in the next one or two days, more businesses will go belly up and ordinary Greeks will suffer.
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