Donald Trump was speaking in West Palm Beach, Fla., on Thursday when The New York Times' response to his threat of a lawsuit hit Twitter.

Trump's lawyer, Marc Kasowitz said in a letter that the newspaper's Wednesday story quoting two women alleging Trump sexually assaulted them was "reckless, defamatory and constitutes libel per se." Kasowitz demanded the paper pull the story from its website, issue an apology and a retraction.

In a response, Times' assistant general counsel David McCraw essentially said the newspaper could not libel Trump because the Republican presidential candidate has himself ruined his reputation.

"The essence of a libel claim, of course, is the protection of one's reputation," McCraw wrote. "Mr. Trump has bragged about his non-consensual touching of women. He has bragged about intruding on beauty pageant contestants in their dressing rooms. He acquiesced to a radio host's request to discuss Mr. Trump's own daughter as a 'piece of ass.'"

Nothing in the Times' story, McCraw wrote, "has had the slightest effect on the reputation that Mr. Trump, through his own words and actions, has already created for himself."

Should Trump disagree, the newspaper's attorney said, "we welcome the opportunity to have a court set him straight."

Trump himself has dispute the Times' story, both in a tweet and at Thursday's rally. At the rally, Trump said the Times is a "failing" newspaper that has sunk to new lows and vowed to sue. He also said he has "evidence" that the allegations are false and that he'd release that evidence at the "appropriate time."