"We wish him well," he said in his first public remarks on the claims against ex-White House staff secretary Rob Porter. "He worked very hard."
His comments come a day after a White House spokesman said they could have better handled the accusations.
It is alleged Mr Porter, 40, gave one ex-wife a black eye while another filed a restraining order. He denies it.
Despite the allegations, he received interim security clearance to act as gatekeeper to the US president. Mr Porter resigned on Wednesday.