WASHINGTON — Ben Carson, the secretary of housing and urban development, told a House committee on Tuesday that he had “dismissed” himself from the decision to buy a $31,000 dining room set for his office last year, leaving the details to his wife and staff.

Mr. Carson offered a rambling, at times contradictory, explanation of the purchase of the table, chairs and hutch, a transaction that turned into a public relations disaster that led President Trump to consider replacing him, according to White House aides.

The hearing, before the House Appropriations subcommittee that determines the Department of Housing and Urban Development’s budget, was supposed to center on the administration’s proposed budget cuts to the agency. Instead it was dominated by questions about Mr. Carson’s judgment, the conduct of his wife, Candy Carson, and son Ben Carson Jr., and Mr. Carson’s initial denial that he was aware of the expenditure, a position he has modified.

“I was not big into redecorating. If it were up to me, my office would look like a hospital waiting room,” said Mr. Carson, who repeatedly told committee members that he had no knowledge of the $5,000 limit imposed on cabinet secretaries for redecorating their offices — despite the release of emails between top aides discussing how to justify getting around the cap.