Why Mr. Trump suddenly latched onto the estimate at this point rather than when casualties were discussed at the earlier meeting remains a mystery to many officials. Some assumed he was influenced by Mr. Carlson or other allies that his re-election would be jeopardized and was looking for cover.

But when the decision came, Mr. Pence, Mr. Pompeo and Mr. Bolton were all out of the White House, and the president did not call them for input. Instead, he told the Pentagon to call off the attack.