Kicking off his diplomatic charm offensive in Paris yesterday, Varoufakis also said Greece did not want the next promised loan tranche of 7.2 billion euros ($8 billion) in funds from the European Union, International Monetary Fund and European Central Bank (ECB).
"It's not that we don't need the money; we're desperate," he said at a joint press conference with his French counterpart Michel Sapin. "What this government is all about is ending this addiction."
With a newly elected anti-austerity government in charge, he said Greece would have to go 'cold turkey' and stop living for the next loan tranche.
Setting out a timetable for a revised debt agreement, which has met with strong German opposition, Varoufakis said if Athens had until the end of the month to come up with detailed proposals, it envisaged reaching an agreement with international partners some six weeks later.
Looking farther ahead, he added: "It will be very sensible to have a new contract for Greece and all nations in place by the end of May."
Varoufakis' plea for time to come up with a realistic solution will be seen as another olive branch to Europe after Prime Minister Alexis Tsipras earlier tried to calm nerves and spooked markets by saying he did not intend to renege on commitments to the EU and IMF.
"It has never been our intention to act unilaterally on Greek debt," Tsipras said in a statement to Bloomberg News.
But he said Greece needed greater leeway to tackle root problems in its economy, such as tax evasion, corruption and policies that favour only a wealthy few.
"We need time to breathe and create our own medium-term recovery programme," he said.
Greece's flurry of diplomacy has seen Tsipras phone European Central Bank chief Mario Draghi late Saturday and book meetings with Italian Prime Minister Matteo Renzi, French President Francois Hollande and European Commission President Jean-Claude Juncker this week.
Varoufakis meanwhile will meet his British and Italian counterparts in London today and Rome tomorrow.
Varoufakis told reporters in Paris that he also wanted to visit Germany, which has shouldered the bulk of Greece's loans and which strongly objects to Athens' plans.
"It is essential that we meet," Varoufakis said, referring to German Finance Minister Wolfgang Schaeuble. "Germany is the powerhouse of Europe."
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