Mr. Trump himself has made clear in other circumstances that he does not trust the intelligence agencies that he is now citing to justify his decision to eliminate General Suleimani. Moreover, given his long history of falsehoods and distortions, Mr. Trump has his own credibility issues that further cloud the picture. All of which means the administration’s failure to provide a consistent explanation has sown doubts and exposed it to criticism.

“If indeed the strike was taken to disrupt an imminent threat to U.S. persons — and that picture seems to be getting murkier by the minute — the case should be made to Congress and to the public, consistent with national security,” said Lisa Monaco, a former senior F.B.I. official and homeland security adviser to President Barack Obama. “Failure to do so hurts our credibility and deterrence going forward.”

Intelligence officials, who spoke on the condition of anonymity to describe sensitive data collection, have said there was no single definitive piece of information about a coming attack. Instead, C.I.A. officers described a “mosaic effect,” multiple scraps of information that came together indicating that General Suleimani was organizing proxy forces around the region, including in Lebanon, Yemen, and Iraq, to attack American embassies and bases.

Several officials said they did not have enough concrete information to describe such a threat as “imminent,” despite the administration’s assertion, but they did see a worrying pattern. A State Department official has privately said it was a mistake for Secretary of State Mike Pompeo to use the word “imminent” because it suggested a level of specificity that was not borne out by the intelligence.

“I have not seen the intelligence, just to be clear, but it is sometimes possible for the reporting of planned attacks to be very compelling even without specificity of time, target or method,” said John E. McLaughlin, a former acting C.I.A. director. “In a sense, that is the story of 9/11. Our reporting gave us high confidence that a big attack was coming — and we so warned — but we were unable to nail down key details.”

Mr. McLaughlin said that the administration may well have had intelligence adequate to compel action, but that it was a separate question whether killing General Suleimani was the most effective response, as opposed to hardening targets or choosing a less provocative option.

John B. Bellinger III, who was the top lawyer for the National Security Council and later the State Department under Mr. Bush, said the president would have the legal authority to strike under the Constitution whether or not there was fear of an imminent attack.