Gen. John F. Kelly, the secretary of homeland security, had dialed in from a Coast Guard plane as he headed back to Washington from Miami. Along with other top officials, he needed guidance from the White House, which had not asked his department for a legal review of the order.

Halfway into the briefing, someone on the call looked up at a television in his office. “The president is signing the executive order that we’re discussing,” the official said, stunned…

Jim Mattis, the new secretary of defense, did not see a final version of the order until Friday morning, only hours before Mr. Trump arrived to sign it at the Pentagon.

Mr. Mattis, according to administration officials familiar with the deliberations, was not consulted by the White House during the preparation of the order and was not given an opportunity to provide input while the order was being drafted. Last summer, Mr. Mattis sharply criticized Mr. Trump’s proposed ban on Muslim immigration as a move that was “causing us great damage right now, and it’s sending shock waves through the international system.”