Speaking two days after the G7 threatened tougher measures against Moscow, the Russian President told a press conference many agreed contracts had been stalled by the sanctions and may have to be torn up.
"Italian companies missed out on a billion euros," he said. "They could have given their enterprises work, created jobs. That didn't happen because of the sanctions."
Putin also said he was convinced sanctions would not be sustained indefinitely. "I count on the fact that... Sooner or later, we will get away from the restrictions that we are encountering today."
Renzi, one of the club members, struck a conciliatory note by stressing that the world wanted Russia back on board to help resolve problems such as Iraq, Syria and Libya.
More From This Section
Active Russian support for efforts to promote peace in Ukraine would "allow us to push the one element of divergence between us off the table," Renzi said.
The Italian leader said Putin had agreed that the Minsk agreement governing a shaky ceasefire in Ukraine had to be the "guiding star, the compass, the reference point" for resolving the crisis.
The tough line adopted by the G7 reflected concern about a recent flare-up in fighting in eastern Ukraine, where the West accuses Russia of providing game-changing military support to pro-Moscow rebels who control parts of two Russian-speaking regions.
Ukraine this week said Russian aid had allowed separatist forces in the east to establish a 42,500-strong fighting force.
Putin says any Russians fighting alongside the rebels are volunteers "answering a call of the heart".