ROME — Over clanking coffee cups at Moscow’s luxurious Metropol hotel in October last year, a close aide to Matteo Salvini, Italy’s most powerful politician and the emerging leader of Europe’s nationalists, sat for more than an hour with a couple of Italian colleagues and some Russian officials.

Unbeknown to them, Italian reporters watched them in the hotel, and in February they published an account in an Italian magazine alleging that the kaffeeklatsch was busy negotiating a complicated plan to secretly finance Mr. Salvini’s hard-right League party with Russian money ahead of the European elections.

The report intrigued analysts and liberal politicians, but its cloudy provenance and Mr. Salvini’s continued denials led the questions to taper off, even as Mr. Salvini’s poll numbers and full-throated support of President Vladimir V. Putin of Russia increased. But on Wednesday, BuzzFeed News published an audio that seemed to confirm the Italian report’s version of the meeting.

The recording was the second to come to light in just months that appeared to reveal how Mr. Putin has actively sought to destabilize the European Union by supporting nationalist, populist parties like the League. In May, the Austrian government fell after a video revealed the leader of Austria’s right wing discussing public contracts in exchange for Russian campaign aid.