"I believe the conditions exist to find an accord with the European institutions," Renzi said at a joint press conference with Greek Prime Minister Alexis Tsipras following talks in Rome.
Renzi also assured Greece's leftist leader of "the greatest possible support, both in terms of bilateral cooperation and in availability for dialogue".
The centre-left Italian leader added: "We all have to read the result of the Greek elections as a message of hope that comes from an entire generation that is demanding more attention and interest in those who have suffered from the crisis.
"The world is calling on Europe to invest in growth, not austerity," he added before joking that the election of Tsipras had been a blessing for him personally.
"Now I will no longer be considered the dangerous lefty (by Brussels)," he said.
The press conference also finished on a light-hearted note with Renzi presenting Tsipras with an Italian tie.
Tsipras - whose fondness for open-necked shirts has been interpreted as a badge of his anti-establishment beliefs - responded by revealing: "I promised I will wear it when we will finally find a viable solution."
Debt swaps not haircuts
Greek Finance Minister Yanis Varoufakis is pushing the idea of debt swaps that would avoid the need for creditors to accept 'haircuts' on the country's €315-billion-euro ($361-billion) foreign debt, while easing the monthly financing burden on the Athens government.
He said Greece's ideas would be put to eurozone finance ministers next week ahead of the summit of EU leaders.
Varoufakis heads to Frankfurt on Wednesday for talks with European Central Bank officials, who were reported Tuesday to be opposing a pivotal part of his plan: a request for bridging finance needed to keep the country solvent until June.
According to the Financial Times, the ECB's opposition could lead to Athens running out of cash at the end of February - a suggestion that may spook markets as much as Tuesday's developments cheered them.
The Greek minister will have another tricky encounter on Thursday, when he will meet Germany counterpart Wolfgang Schaeuble in Berlin in what will be a key test of whether his proposals have any chance of being accepted by the EU's leading powers.
Athens stocks soar
The Greek initiative was interpreted by markets on Tuesday as reducing the likelihood of any unilateral debt cancellation, which would entail a risk of reigniting the kind of financial turmoil that has severely damaged leading economies since 2007.
Led by the Athens bourse, which closed up more than 11 percent, stock markets across Europe rose on the news, as did Wall Street.
"After a week of trading insults and threats it looks like the eurozone paymasters and the new Greek government are finally ready to compromise," said Kathleen Brooks, research director at trading site Forex.com.
The Greek government denied the debt swaps proposal represented a climbdown from election promises to force a renegotiation of its debt terms.
"If we need to use euphemism and the tools of financial mechanisms to get Greece out of its debt-slavery, we will do it," a spokesman said.
The Greek plan would involve swapping some of the country's current bonds for new ones under which repayments would be linked to economic growth rates.
Greek bonds owned by the European Central Bank would become "perpetual", or open-ended, removing the need to make regular repayments at fixed intervals.
German Chancellor Angela Merkel was non-committal about the Greek proposals. "It is clear the Greek government is still establishing its position," she said. "We await their proposals and there will be time enough to discuss them."
Privately, German officials said there was "little room for manoeuvre" on the debt conditions.
Greece's debt is worth 1.75 times the country's entire annual economic output. Because of severe spending cuts, the government now raises substantially more in taxes than it pays to fund services, but that surplus is more than wiped out by the cost of servicing the debt.
US President Barack Obama on Sunday appeared to side with Greece by warning of the dangers of "squeezing" an economy in the grip of recession.
Next stop Paris
Tsipras has dismissed the "troika" system monitoring Greece's economy - the International Monetary Fund, European Commission and ECB - as lacking legal status, and blames Germany for driving the tough austerity programmes that his radical left government has pledged to end.
But he also says Greece has no intention of not meeting its outstanding obligations to the bailout creditors.
The new premier is due in Brussels on Wednesday and will also visit Paris in search of support from France, the eurozone's second-biggest economy and, like Italy, a critic of EU 'austerity'.