The associate, Gianluca Savoini, is under investigation by Milan prosecutors for alleged international corruption stemming from reports that he discussed the financing plan during a meeting with Russian officials in Moscow last year, months after the right-wing League came to power in a coalition government with the 5-Star Movement.
Salvini had initially distanced himself from Savoini, denied taking any money from Russia and brushed off opposition demands to respond in Parliament, calling the whole case a "fantasy" as recently as Monday. But as calls increased for him to refer to Parliament and extended to his populist 5-Star coalition partner, he agreed Tuesday.
Salvini said he would respond to lawmakers "about everything humanly knowable" during a regular question-and-answer appearance in Parliament.
"Certainly I'll go to Parliament. It's my job," he said.
However, no date was immediately set. Opposition lawmakers demanded for Salvini to agree to a special appearance and not just answer off-the-cuff questions during a routine event.
They said the issue demanded a dedicated session that would start with a prepared speech by Salvini and move onto debate.
The Milan investigation began after Italian newsweekly L'Espresso reported in February that Savoini had sought millions of dollars in financing for the League during a meeting with Russian officials in Moscow last year. The case made headlines again last week after BuzzFeed News published audio of the meeting.
Savoini on Monday was questioned by Milan prosecutors but invoked his right not to respond, according to his lawyer, Lara Pellegrini. She said he might respond later once the defense has been provided with details of the investigation.
Savoini denies wrongdoing, she said. She declined to answer when asked if he attended the meeting caught on tape.
Chief prosecutor Francesco Greco said Tuesday there was "absolutely no" plan at the moment to summon Salvini for questioning, the ANSA news agency said.
The investigation has become the latest issue to divide Italy's uneasy government coalition. On Sunday, Premier Giuseppe Conte distanced himself from Savoini and blamed a Salvini adviser for having intervened to invite him to a dinner that Conte hosted for visiting Russian President Vladimir Putin on July 4.
Conte's other deputy premier, 5-Star Leader Luigi Di Maio, called Tuesday for Salvini to appear in Parliament to respond as did the 5-Star president of the lower chamber, Roberto Fico.
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