Interior Minister Salvini, an admirer of Russian President Vladimir Putin who has denied taking Moscow's money, called a national security council meeting that coincided with the timing of the Senate's Russia questions.
The League's government coalition partner, the Five Star Movement (M5S), which was elected on a strong anti-corruption platform, boycotted the session over Salvini's refusal to attend.
Prosecutors are probing a meeting between Salvini ally Gianluca Savoini, two other Italians and three Russians, during which a deal was discussed to covertly divert $65 million (58 million euros) to the League by means of discounted Russian oil transactions through intermediaries.
Matteo Salvini on the visit to Moscow in October 2018. Photo: Mladen Antonov/AFP
Savoini, whose voice was identified on a covert recording of the talks in Moscow, has invoked his right to remain silent before prosecutors, Italian media reported.
The first stories of the October meeting at a Moscow hotel appeared in the Italian press in February.
But the publication earlier this month by online news website Buzzfeed of a transcript of the talks — taken from an audio recording — pushed it back onto centre stage after being widely reported in Italy.
Buzzfeed said it was not clear whether the proposed deal ever came to fruition.
After Salvini's refusal to attend, prime minister Conte, a “compromise” leader agreed upon by both coalition parties last year, was called upon but was unable to answer questions concerning Salvini's Russian contacts and a dinner the pro-Russian minister had with Savoini the night before the Moscow meeting.
Conte had asked Salvini to attend but was obliged to tell senators that he had “not received information from the competent ministry”.
“At this stage of the inquiry, no element weighs upon the trust I have in members of the government,” Conte said, adding that no one in the administration had distanced themselves from the “agreed common position” on Russia.
Former journalist Savoini, 56, is married to a Russian and is president of the Lombardy-Russia association. He is considered one of the League's main contacts with Russia.
League Senator Massimiliano Romeo called for a probe into the financing of all Italian political parties, alleging that other parties had more to hide.
Salvini has made no secret of his admiration for Vladimir Putin, who visited Italy at the start of the month.
During his visit, Putin referred to a cooperation agreement between his United Russia party and Salvini's League.
But Salvini says his support for Putin and his fight to overturn European sanctions imposed against Russia, comes “for free”.