Talks got underway between eurozone finance ministers in Brussels on Monday, but Padoan said both sides "stuck to their positions", according to a report on Ansa.
Greece's current bailout arrangements expire at the end of February, meaning that it risks bankruptcy unless it can reach agreement on a new financial aid programme with its European neighbours.
In quotes published by Rai News, Padoan said Greece leaving the euro was "out of the question" and that he was convinced that, ultimately, "common ground will be found".
Greek borrowing prices soared and the euro sank against the dollar hours after the radical leftist government on Monday refused a demand by eurozone partners that it apply for an extension to its EU bailout.
Eurogroup head Jeroen Dijsselbloem, who is also Dutch finance minister, gave the country 48 hours to request the extension to the bailout programme.
Pressure was mounting to agree a deal on Tuesday as an Economic and Financial Affairs Council (Ecofin) meeting wrapped up.
"If this programme is not concluded in an orderly manner a difficult situation will ensue...But there is no sense in speculating over what will happen," German Finance Minister Wolfgang Schäuble said at a press conference.
Several EU countries - including Germany - require that any agreement with Greece be approved by their own parliaments, leaving the time available to reach a compromise even shorter.
The picture is complicated further by the apparent disunity between Greek Finance Minister Yanis Varoufakis and his Prime Minister, Alexis Tspiras.
Varoufakis appeared ready to make a deal last Thursday, but rejected the other countries' offer after speaking with Tsipras at the last minute.
Varoufakis also incurred the wrath of Padoan last week by comparing Italy's problem with its large public debt to those of Greece.
Despite the difficulties, Varoufakis said the different sides would find agreement in time to set up a next meeting for Friday.