She said Mr. Conyers suspected her of cheating after he went through her computer. She said that she had tried to call the police, but that Mr. Conyers took her phone and then chased her into the kitchen, where she grabbed a knife and told him to leave. She also said Mr. Conyers took the knife and swung it at her, cutting her arm, according to NBC News.

Mr. Conyers said in the interview on Wednesday that his girlfriend had eventually called the police. However, the Los Angeles County District Attorney’s Office, citing a “lack of independent witnesses,” concluded that it “could not be proven beyond a reasonable doubt that the victim’s injury was not accidentally sustained” while Mr. Conyers was trying to take away the knife, NBC reported.

Mr. Conyers, who describes himself as “a partner at Detroit’s first minority-run hedge fund,” said that he wanted to be honest and transparent about the incident and that he felt remorseful.

“I apologize, and I am regretful for any part I played in escalating the altercation,” he said.

Representative John Conyers Jr. announced Tuesday that he would leave Congress, and he endorsed his son to succeed him. By trying to keep his Detroit-area seat in the family, Mr. Conyers, 88, the longest-serving African-American representative in history, may have touched off a family feud. His great-nephew Ian Conyers, a state senator in Michigan, had already said he plans to run in a special House election.

But John Conyers III said Wednesday that he was not sure he wanted to run because he did not want to deal with “public life,” which often comes with “unnecessary grief.”

“I didn’t ask my dad to say that I was going to run because I don’t know if I am going to run,” Mr. Conyers said. “I was extremely caught off guard by his endorsement. This is what he wants. Who am I to tell him what he wants?”