On Saturday, he did not mention his successor, Mick Mulvaney, by name. But his comments appeared to pin the blame for the fast-moving impeachment inquiry on Mr. Trump’s embattled acting chief of staff, who said at a news conference last week that aid to Ukraine had been withheld because the president wanted to pressure the country to investigate his political rivals, only to later backpedal. And Mr. Kelly framed Mr. Trump himself as a careening leader who needed to be controlled by his aides.

“I have an awful lot of, to say the least, second thoughts about leaving,” Mr. Kelly said. “It pains me to see what’s going on, because I believe if I was still there or someone like me was there, he would not be kind of, all over the place.”

During his early days as chief of staff, Mr. Kelly, a retired four-star general, was credited for bringing order to a chaotic West Wing. But by the end, he found the task of managing Mr. Trump to be impossible, and often complained to colleagues that the role was thankless.

In his comments on Saturday, however, Mr. Kelly cast his management style as a better model than what has followed.

“Don’t hire someone that will just nod and say, ‘That’s a great idea, Mr. President,’” Mr. Kelly said, adding that any successor needed to tell Mr. Trump that “you either have the authority or you don’t, or Mr. President, don’t do it.”