Omarosa Manigault Newman released a secret recording on Thursday that she said backed her claim that President Trump’s daughter-in-law had offered her a $15,000-a-month contract in exchange for her silence about her time as a White House adviser.

The audio, released during an interview on MSNBC, is the latest in the trickle of recordings that Ms. Manigault Newman has made public to bolster the credibility — and sales — of her tell-some book, “Unhinged,” about her tenure at the White House.

In the book, she claimed that the Trump 2020 campaign, which is partly overseen by Lara Trump, who is married to Mr. Trump’s son Eric, offered her a salary equal to what she had earned before being fired from the White House in December.

Ms. Trump noted on the tape, which Ms. Manigault Newman said was recorded days after she was fired, that the money would come from campaign donors.