Allies of Mr. Trump say his sense of being surrounded by hostile forces will be relieved once his own appointments fill the thousands of political jobs that have not yet been filled. But people close to Mr. Trump concede that the White House’s sluggish hiring process, in which insufficient work was done to tap people for key deputy roles at major agencies during the transition process, is a large part of the problem.

“Any new administration takes a while to get their sea legs,” said Charlie Black, a veteran Republican lobbyist. But he added that for Mr. Trump’s administration, “a big part of it is the lack of personnel political appointees around the government.”

In the meantime, Mr. Black and other Republicans said that Mr. Trump had to avoid the trap of fighting all fights, no matter how small.

“The Trump team needs to better stay on the offense with their reform agenda, take out the trash, and get on with governing,” said Scott Reed, the top political strategist for the United States Chamber of Commerce, in a typical critique.

Mr. Trump’s aides were heartened by his relative calm even amid the flap around Mr. Sessions. And he stayed on message during his appearance on the Gerald R. Ford and on Friday in an appearance in Florida, declining to weigh in then as new reports emerged about previously undisclosed meetings between additional advisers and the Russian ambassador.

Mr. Trump is not one to spare the blame when he has hit difficult patches in the past, and his rebuke of Mr. Sessions reflected that. So did his public jab at his press secretary, Sean Spicer, for his attempt to trace leaks from his communications staff members by examining their cellphones. Mr. Trump told Fox News that he personally would have done that type of search “differently.”