Howard Lutnick, President Trump’s commerce secretary, will face questions Wednesday from the House Oversight Committee over his ties to Jeffrey Epstein, the convicted sex offender.

Mr. Lutnick is one of the highest-profile cabinet members to come under scrutiny in connection with Mr. Epstein. The commerce secretary’s name appeared in more than 250 documents in the Epstein files released by the Justice Department, a review by The New York Times found.

Mr. Lutnick lived next door to Mr. Epstein on the Upper East Side of Manhattan for over a decade. Until recently, he had claimed to have not been in the same room with Mr. Epstein after an encounter in 2005. But millions of documents that were released by the Justice Department earlier this year showed that Mr. Lutnick had traveled to Mr. Epstein’s private island in 2012.

The documents suggest Mr. Lutnick had another encounter with Mr. Epstein at his house in 2011, years after Mr. Lutnick claimed to have cut ties with him. The records also indicated that the men invested in the same privately held company together and dealt with each other on neighborhood and philanthropic issues.

Mr. Epstein, who was convicted in Florida in 2008 of soliciting prostitution from a minor, died in a Manhattan jail in 2019 while being held on federal sex-trafficking charges.

Mr. Lutnick has received questions from lawmakers about his connections with Mr. Epstein in congressional hearings on other topics, first in February and again last month.

All Democrats and some Republicans on the Oversight Committee signaled that they would try to force a vote on a subpoena for Mr. Lutnick. But the panel’s Republican chairman, Representative James R. Comer of Kentucky, said that Mr. Lutnick had volunteered to testify.

The Commerce Department said in a statement on Wednesday that Mr. Lutnick looked forward to “putting to rest the inaccurate and baseless claims in the media.”

Though the committee’s investigation into Mr. Epstein and the Justice Department’s handling of the case against him has sprawled to include a number of political figures, Mr. Lutnick is the first current Trump administration official to testify before the panel.

The committee also issued a subpoena to Pam Bondi, the former attorney general who Mr. Trump fired last month, before she was dismissed from her position. She has not yet appeared for a deposition.

Questions by lawmakers in the closed-door session on Wednesday could touch on Mr. Lutnick’s former nanny. The files showed that Mr. Epstein expressed an interest in meeting the nanny in 2013 and had her résumé sent to him. It is not clear if they ever met.

Mr. Lutnick said in February that he did not know if the nanny had met Mr. Epstein, or if she was one of the nannies Mr. Lutnick had brought to the island. Mr. Lutnick has four children.

In October, Mr. Lutnick said in a podcast interview that he had decided after a 2005 incident not to associate with Mr. Epstein, after Mr. Epstein alluded to his sexual encounters with women while giving Mr. Lutnick and his wife a tour of his house.

“My wife and I decided that I will never be in the room with that disgusting person ever again,” Mr. Lutnick said on the podcast, “Pod Force One.” “So I was never in the room with him socially, for business or even philanthropy.”

But in a congressional hearing in February, Mr. Lutnick told lawmakers that he not only met with Mr. Epstein after that encounter, but that he and his family also traveled to his private Caribbean island, Little St. James, in 2012 for lunch. Mr. Lutnick was traveling aboard his yacht and accompanied by his wife, children, nannies and another family.

The visit took place four years after Mr. Epstein had pleaded guilty in Florida to soliciting prostitution from a minor as part of a plea bargain with federal prosecutors.