The comments came after Putin met with Prime Minister Matteo Renzi.
The Russian leader later met with Pope Francis, who gave Putin a medallion depicting the angel of peace, Vatican spokesman Federico Lombardi said. The Vatican called it "an invitation to build a world of solidarity and peace founded on justice."
Putin, who arrived at the Vatican an hour behind schedule, gave the pope an embroidery of the Cathedral of Christ the Savior in Moscow.
Lombardi said the pontiff and President talked for 50 minutes about the violence in Iraq and Syria and the crisis in Ukraine.
The Pope has angered Catholics in Ukraine because, in his search for peace, he has failed to condemn Russian actions in the country.
Both Putin and Renzi said full implementation of an accord reached in February in Minsk, Belarus, is critical. The accord includes a ceasefire and also calls for the removal of heavy weapons by both sides, along with other measures.
"The Minsk agreement is the compass by which we should be guided," Renzi said. "It is our polar star."
Putin, too, called for "full implementation of the Minsk agreement." But some international officials doubt that Russia is respecting the accords.
A readiness to strengthen sanctions
Just this week, leaders of the G7 group of industrialized countries meeting in Germany were sharply critical of Russia's actions in Ukraine, one of its neighbors to the west and a former republic in the Soviet Union.
German Chancellor Angela Merkel said at the meeting that other countries were "ready, should the situation escalate -- which we don't want -- to strengthen sanctions if the situation makes that necessary."
And President Barack Obama, in unusually harsh language, accused Putin of doing his own country serious harm.
"Ultimately, this is going to be an issue for Mr. Putin," Obama said. "He's got to make a decision: Does he continue to wreck his country's economy and continue Russia's isolation in pursuit of a wrongheaded desire to recreate the glories of the Soviet empire? Or does he recognize that Russia's greatness does not depend on violating the territorial integrity and sovereignty of other countries?"
But Putin said Wednesday in Italy that the sanctions cut both ways. Russia's trade with Italy had fallen sharply, he said. And 400 Italian firms are working in Russia, he said.
"Italian companies did not receive millions of dollars ... because of the sanctions," he said.