Hunter Biden, President Biden’s son, withdrew a lawsuit against Fox News on Sunday that had accused the network of violating a revenge porn law by sharing explicit photos and videos of him without his permission.

Mr. Biden’s decision to drop the lawsuit, in a one-page motion filed by his lawyers in New York Supreme Court in Manhattan, came on the same day that his father announced he would no longer seek re-election.

The lawsuit involved “The Trial of Hunter Biden,” a mini-series that appeared in 2022 on the streaming service Fox Nation. The series imagined a prospective criminal trial of Mr. Biden that involved fictional charges, and it integrated actual images of Mr. Biden in the nude and engaged in sex acts that had been discovered on a laptop he abandoned at a repair shop in Delaware.

“The Trial of Hunter Biden” was removed from Fox Nation in April after lawyers for Mr. Biden contacted the network demanding that it be taken down.

Fox News had earlier rejected the legal reasoning behind Mr. Biden’s lawsuit, calling it “entirely politically motivated” and “devoid of merit.”

A representative for Mr. Biden did not immediately return a request for comment on Monday.

In June, Mr. Biden was found guilty on three felony counts to buying a firearm. He is set to stand trial later this year on tax evasion charges.