"In general, I am really positive after this meeting," Renzi said after the talks in Milan which were also attended by the leaders of Britain, France and Germany.
"I hope this spirit (of dialogue) … will continue," he said, citing a sense of urgency to solve a conflict which has cost more than 3,600 lives.
A ceasefire and peace accord, agreed in early September in Minsk between Kiev and pro-Russian rebels in eastern Ukraine, has held so far but there have been many breaches.
French government officials said separately that Putin and Poroshenko would hold another meeting later on Friday with French President Francois Hollande and German Chancellor Angela Merkel.
Renzi also said that the breakfast meeting had made enough progress for additional talks but gave no specifics.
For his part, British Prime Minister David Cameron also described the meeting as positive because President Putin had "said very clearly that he does not want a frozen conflict, a divided Ukraine."
"If that is the case," however, Putin must now live up to his commitments to help implement the Minsk accords and end Russian intervention in Ukraine.
Failing, the European Union would have not choice but to leave tough sanctions against Russia in place, Cameron said.