Medvedev had called on Europeans to "punish" their "stupid" governments for opposing Moscow over its war in Ukraine.
Italian politicians have expressed concern about the possibility of Russian "interference" in next month's parliamentary elections.
Comments by former Russian President Dmitry Medvedev have sparked controversy and worry ahead of the vote on 25 September.
On Thursday, Medvedev called on European citizens to "punish" their "stupid" governments for opposing Moscow, amid the war in Ukraine.
"We would like to see European citizens not only outraged at the actions of their governments ... but to hold them to account and punish them for their obvious stupidity," he wrote on Telegram.
"Take action, European neighbours. Don't remain silent. Demand accountability," he added.
Italy -- led by outgoing Prime Minister Mario Draghi -- has so far supported Ukraine unreservedly since the start invasion, providing arms and humanitarian aid.
But the country's stance could change if the more pro-Russian right-wing coalition wins the elections.
Medvedev's comments were slammed by Italian Foreign Minister Luigi Di Maio, who warned of "Russian government interference in the elections".
Democratic Party Enrico Letta also stated that Moscow is trying to "change the position of Italian foreign policy, which since the beginning has been very clear alongside the EU and NATO".
"We must reconfirm this choice, it is clear that the election on 25 September will also be about this," Letta added, criticising right-wing parties for remaining silent.
The former Italian prime minister also called on the far-right League to abolish a 2017 agreement it signed with the United Russia party of President Vladimir Putin.
League leader Matteo Salvini had considered travelling to Moscow after the start of the Russian invasion before cancelling plans.
He defended himself on Friday, stating that he had "not been to Russia for years" and that "Russia does not have the slightest influence on the Italian elections".