President Trump’s longtime lawyer, Michael D. Cohen, secretly recorded a conversation with Mr. Trump two months before the presidential election in which they discussed payments to a former Playboy model who said she had an affair with Mr. Trump, according to lawyers and others familiar with the recording.

The F.B.I. seized the recording this year during a raid on Mr. Cohen’s office. The Justice Department is investigating Mr. Cohen’s involvement in paying women to tamp down embarrassing news stories about Mr. Trump ahead of the 2016 election. Prosecutors want to know whether that violated federal campaign finance laws, and any conversation with Mr. Trump about those payments would be of keen interest to them…

Rudolph W. Giuliani, Mr. Trump’s personal lawyer, confirmed in a telephone conversation on Friday that Mr. Trump had discussed the payments with Mr. Cohen on the tape but said the payment was ultimately never made. He said the recording was less than two minutes and demonstrated that the president had done nothing wrong.