“We fought very hard to get Otto Warmbier back,” Mr. Trump added. “And when we came back, he was in very, very bad condition.”

The lawsuit details the abuse inflicted on Mr. Warmbier, 22, saying that after he was returned to Ohio in a coma, doctors diagnosed “an extensive loss of brain tissue” that was “caused by the cessation or severe reduction of blood flow to the brain.” He had a “scarred wound” on his left foot and his teeth had been misaligned, “forced into abnormal positions.”

When Mr. Warmbier’s parents boarded the plane that carried him to Cincinnati, the suit said, “they were stunned to see his condition.”

“Otto was blind and deaf,” the suit said. “He had a shaved head, a feeding tube coming out of his nose, was jerking violently and howling, and was completely unresponsive to any of their efforts to comfort him.”

The suit does not include new information or theories about what caused Mr. Warmbier’s injuries. It cites Mr. Trump’s statement in September 2017 that he was “tortured beyond belief by North Korea,” as well as a report in The New York Times in June, citing a senior American official, which said Mr. Warmbier had been repeatedly beaten.

Mr. Warmbier, a junior majoring in economics at the University of Virginia, was detained at the airport in Pyongyang on Jan. 2, 2016, as he tried to leave North Korea after a five-day visit to the country with a tour group. North Korean authorities accused him of ripping down a propaganda poster from a restricted area of his hotel in Pyongyang.

During a televised news conference a month later, Mr. Warmbier confessed to taking down the poster, saying he had done so at the behest of Friendship United Methodist Church near Cincinnati, which promised him a used car as payment. He also said he had been encouraged to do so by Z, a secret society at the University of Virginia that has ties to the C.I.A.