WASHINGTON — Ben Carson, the secretary of housing and urban development, is attempting to cancel a $31,000 order for a customized hardwood dining room table, chairs, sideboard and hutch the day after the chairman of the House Oversight Committee announced an investigation into the refurbishment of his HUD office.

“At the request of the secretary, the agency is working to rescind the order for the dining room set,” Armstrong Williams, Mr. Carson’s business manager and an informal adviser, said on Thursday.

He added, however, that “it might not be possible.”

On Tuesday, Raffi Williams, a department spokesman said Mr. Carson had no problem with the order and no intention of returning the table. But early Thursday, Mr. Williams said the secretary, who was sharply criticized for the purchase at a time when his agency is facing $6.8 billion in budget cuts requested by the White House, seemed to change his mind.

“Nobody was more surprised than me,” about the order, Mr. Carson said in a statement.

But several department officials, speaking on condition of anonymity for fear of retaliation, said it would have been highly unusual for Mr. Carson not to have been told that a significant section of his office suite was about to be upgraded.