Robert S. Mueller III, the former special counsel who investigated ties between President Trump’s campaign and Russia, was diagnosed with Parkinson’s disease four years ago, his family said in a statement on Sunday.

In recent months, Mr. Mueller, a former F.B.I. director, has had difficulty speaking and experienced mobility issues, people familiar with his condition said. As a result, Mr. Mueller cannot comply with a request to testify this week before a congressional committee investigating the government’s handling of the Jeffrey Epstein investigations, they said.

“Bob was diagnosed with Parkinson’s disease in the summer of 2021,” the family said in a statement to The New York Times. “He retired from the practice of law at the end of that year. He taught at his law school alma mater during the fall of both 2021 and 2022, and he retired at the end of 2022. His family asks that his privacy be respected.”

The statement from the family came after the House Oversight and Government Reform Committee said it would subpoena him to testify on Tuesday as part of its inquiry into the federal government’s handling of the investigations and prosecutions of the financier Mr. Epstein.

The committee wanted to question Mr. Mueller, 81, about the F.B.I.’s handling of the Epstein investigation when he served as its director from 2001 to 2013.

Mr. Mueller became F.B.I. director two weeks before the Sept. 11, 2001, terrorist attacks. During his tenure leading the bureau, he had a reputation as a commanding figure, known for not only his ability to remember minute facts about major national security cases but also his physical stamina.