In May, Donald J. Trump was criminally convicted of covering up a hush-money deal with the porn star Stormy Daniels.

By July, he had tried to hush her up again, a document newly released by her lawyer shows.

The first effort to buy Ms. Daniels’s silence stemmed from the final days of the 2016 presidential campaign, when she accepted $130,000 to keep quiet about a sexual encounter she said she had with Mr. Trump, a payoff that eventually led to the former president’s conviction.

The new and unsuccessful push to keep Ms. Daniels quiet — coming amid Mr. Trump’s latest White House run — arose from a discussion over a debt she owed him in a separate civil case. Ms. Daniels had sued Mr. Trump for defamation, but the courts dismissed the case and ordered her to pay his legal fees.

Ms. Daniels eventually offered to pay about $600,000, slightly short of what Mr. Trump’s lawyer claimed she owed.

Mr. Trump’s lawyer, Harry J. Ross, agreed to accept the lower amount on one condition: that Ms. Daniels stop talking about the former president, both in public and privately. It would have been, in essence, a hush-money discount.

Mr. Ross conveyed the proposal to Ms. Daniels’s legal team in July, in a letter suggesting she sign a nondisclosure agreement. The deal would have effectively barred her from criticizing Mr. Trump or discussing any encounter they may have had.