The parents of Seth Rich, the young Democratic aide whose unsolved murder became grist for right-wing conspiracy theories about the 2016 presidential race, filed a lawsuit on Tuesday against Fox News, claiming that the network’s coverage helped fuel damaging rumors about their son.

The suit, filed in the Federal District Court in Manhattan, accuses Fox News of “extreme and outrageous” conduct. It claims that a reporter for the network, Malia Zimmerman, and a regular Fox News guest, Ed Butowsky, intentionally fabricated a story that portrayed Mr. Rich as the person who leaked thousands of internal Democratic National Committee emails to WikiLeaks in 2016, which released them to the public in an act that proved damaging to Hillary Clinton’s presidential campaign.

That story, published on the Fox News website on May 16, 2017, implied that the murder of Mr. Rich on the streets of Washington occurred in retaliation for his having leaked the emails. No evidence to support that theory emerged during an investigation by the Washington Metropolitan Police Department, and Mr. Rich’s family said they believed that Mr. Rich, then 27, was killed during an attempted robbery.

Fox News retracted the article a week after it was published, saying that it did not meet network standards.