WASHINGTON — Ben Carson, the secretary of housing and urban development, took responsibility on Thursday for buying a $31,000 dining room set for his office, two days after saying his wife and assistant oversaw a purchase that has jeopardized his place in President Trump’s cabinet.

Mr. Carson faced withering criticism from Democrats on the Senate Banking Committee, which oversees the Department of Housing and Urban Development. One senator, Sherrod Brown of Ohio, suggested that he regretted being one of the few Democrats to support the secretary’s nomination a year ago.

“I voted to confirm you,” said Mr. Brown, who is up for re-election this year. “Four other Democrats on this committee voted to confirm you. I’m not sure I made the right decision.”

In recent days, Mr. Carson’s aides have repeatedly advised him to apologize for the purchase, arguing that doing so was the only way to move on, according to several people with knowledge of the situation. But Mr. Carson, who has privately fumed about what he regards as the unfairness of being singled out for criticism, resisted doing so until Thursday’s hearing, when one of the panel’s Republicans, Senator Tim Scott of South Carolina, gently prodded him to be more contrite.