He raised the possibility that Mr. Putin is “delusional” and “breaks all the rules” by, in just one instance, sending heavy nuclear-capable bombers off the U.S. coast.

“The person who threatened on their national news one night to turn America to radioactive ash was promptly promoted by Putin and put into the government ministry of information,” said Mr. Mattis, who would have a critical role in checking Mr. Putin’s military moves. “So this is where miscalculations can happen.”