CNN  — 

Members of the “Central Park Five” sued former President Donald Trump on Monday over “false and defamatory” statements they allege he made about their 1989 case during a presidential debate last month.

The five men claim in a federal lawsuit that Trump knew he was acting with “reckless disregard” for the truth when he said during the September debate with Vice President Kamala Harris that they pleaded guilty to crimes connected to the beating and raping a woman in New York City, and that the five teenagers “badly hurt a person, killed a person” in the attack.

“Defendant Trump’s statements were false and defamatory in numerous respects,” attorneys for the men, now all in their 50s, wrote in the lawsuit filed in federal court in Philadelphia. “Plaintiffs never pled guilty to the Central Park assaults. Plaintiffs all pled not guilty and maintained their innocence throughout their trial and incarceration, as well as after they were released from prison.”

“None of the victims of the Central Park assaults were killed,” the lawyers for Yusef Salaam, Raymond Santana, Kevin Richardson, Antron Brown and Korey Wise wrote.

Trump campaign spokesperson Steven Cheung called the lawsuit “just another frivolous, Election Interference lawsuit” that he claimed was brought to “distract the American people from Kamala Harris’s dangerously liberal agenda and failing campaign.”

The men are seeking compensatory and punitive damages. The suit also claims that Trump’s comments placed them in a false light and caused them to “suffer severe emotional distress.”

The group was pressured into giving false confessions in the case. They were exonerated in 2002 when DNA evidence linked another person to the crime. The teenagers sued the city, and the case was settled in 2014.

Trump has long been outspoken on the case, which rocked New York in the late 1980s during a time when he was a leading figure in the city’s real estate and celebrity scenes. At the time, Trump took out full-page ads that ran in several New York City newspapers that read in all-caps, “BRING BACK THE DEATH PENALTY. BRING BACK OUR POLICE!”

His comments last month came in response to Harris bringing up the ad during a portion of the debate dedicated to race and politics in the US.

“Let’s remember, this is the same individual who took out a full-page ad in The New York Times calling for the execution of five young Black and Latino boys who were innocent, the Central Park Five,” Harris said. “Took out a full-page ad calling for their execution.”

In this May 2019 photo, Kevin Richardson, Antron Mccray, Raymond Santana Jr., Korey Wise, and Yusef Salaam, collectively known as the "Central Park Five", attend the World Premiere of Netflix's "When They See Us" at the Apollo Theater in New York City.

One of the ads Trump purchased was included as an exhibit in the lawsuit.

The former president has sought to project a tough-on-crime persona during his three White House bids, and the debate comments underscored his willingness to invoke racially and politically charged criminal cases in US history in that pursuit.

Trump has continued to be critical of the case as he’s moved into politics in recent years. In October 2016, then-candidate Trump stood by his actions during the time of the case, telling CNN, “They admitted they were guilty.”

And in 2014, Trump wrote in an op-ed in the New York Daily News that New York City’s $41 million settlement with the five men was “a disgrace.”

This story has been updated with additional details.

CNN’s Kate Sullivan contributed to this report.