Enrico Letta, who is now chairman of the Middle-left Democratic Party, and Matteo Renzi, another former Prime Minister, called for an investigation by the Italian Parliament's intelligence agency.
"Salvini has to explain the relationship between the league and the Kremlin. We want to know whether it was Putin who has overthrown the Draghi government," said Mr. Letta. "If that were the case, it would be of the greatest importance."
Italy's unruly political landscape was shaken by claims that were first raised on Thursday by the daily newspaper La Stampa that an official of the Russian embassy in Rome had pushed Mr. Salvini to determine whether he would withdraw the government coalition in May.
The contact said reported between Oleg Kostjukow, a political officer of the message, and Antonio Capuano, a consultant of Mr. Salvini, who was behind a failed attempt to send the league to a "peace mission" to Moscow in May.
la Stampa said that she was looking for her story on reports of the Italian secret services.
Mr. Salvini called the claims "fake news" and insisted that he believed that the communication channels with Moscow should be kept open, but his party was "with the West and democracy".
But the Italian foreign minister called the claims "deeply worrying".
"I say Salvini that he has to explain his relationships with Russia," said Luigi di Maio.
The coalition, led by the former President of the European Central Bank, Mario Draghi, broke out dramatically last week after the league and two other parties, including Silvio Berlusconi's Forza Italia, withdrawn their support.