The way the strike was handled has drawn scrutiny from Democrats and some Republicans. Critics say the decision was hasty, considering the risk of all-out war. They also question whether the intelligence that prompted the action was as clear-cut and alarming as the White House has said, and see the move as doing little to further U.S. interests in the region.

Mr. Trump, after the strike, told associates he was under pressure to deal with Gen. Soleimani from GOP senators he views as important supporters in his coming impeachment trial in the Senate, associates said.

At first, White House officials said, there wasn’t unanimity among advisers over the wisdom of targeting Gen. Soleimani. Intelligence, however, pointed to the prospect—initially described as “imminent” by administration officials—of more Iranian-backed attacks on U.S. military personnel in the region, the officials said.