"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 which favour only a wealthy few.
"We need time to breathe and create our own medium-term recovery programme," he said.
Today's meeting is likely to have been one of the easiest of the many Varoufakis has ahead of him, as Sapin has already said the EU should be open to restructuring Greek debt or extending the bailout terms.
Amid the flurry of diplomacy, Tsipras spoke with European Central Bank chief Mario Draghi night and has booked in meetings with Italian Prime Minister Matteo Renzi, French President Francois Hollande and European Commission President Jean-Claude Juncker this week.
German Chancellor Angela Merkel ruled out fresh debt relief, telling the Hamburger Abendblatt daily: "There has already been voluntary debt forgiveness by private creditors, banks have already slashed billions from Greece's debt."
"I do not envisage fresh debt cancellation," she said, as a new poll for broadcaster ZDF found 76 percent of Germans oppose any debt reduction.
Portuguese Prime Minister Pedro Passos Coelho and Finnish Prime Minister Alexander Stubb also oppose any debt relief. Despite a restructuring in 2012, Greece is still lumbered with a debt pile of more than 315 billion euros, upwards of 175 percent of gross domestic product (GDP) — an EU record.
But in its first week in power, the government scrapped the privatisation of Greece's two main ports and the state power company and announced a major increase in the minimum wage.
Varoufakis has further raised the stakes by refusing to continue talks with the much-hated EU-IMF negotiating team known as the "troika", saying they want to deal only with individual governments.
Martin Schulz, the German head of the European Parliament, said this position was "irresponsible", but the Greek minister argued it was pointless dealing with the troika since they are not authorised to renegotiate the bailout.
"Why should they waste their energy and their time?" he told the To Vima weekly.
Varoufakis had his strained meeting with Jeroen Dijsselbloem, who represents finance ministers from the 19-nation eurozone. Dijsselbloem warned Athens that "taking unilateral steps or ignoring previous arrangements is not the way forward".
Greece has been promised another 7.2 billion euros in funds from the EU, IMF and European Central Bank, but this is dependent on the completion of a review of reforms at the end of February.
Varoufakis has said his government does not want the loans, but there are concerns Greece cannot survive without them. A particular issue is Greece's banks, which are helping the state stay afloat by purchasing its treasury bills — and which are being supported by the ECB.
Bank of Finland governor Erkki Liikanen, who sits on the ECB's governing council, said it cannot continue lending Greece money unless Athens extends its bailout programme.
"Greece's programme extension will expire at the end of February so some kind of solution must be found, otherwise we can't continue lending," he told
public broadcaster Yle.
The stunning success of Tsipras' hard-left Syriza party in last Sunday's polls sent shockwaves through the continent and has lent encouragement to other anti-austerity parties. Tens of thousands of people took to the streets of Madrid in support of the Spanish party Podemos, which has been surging in polls ahead of elections later this year.