Several issues might delay any immediate military action, officials said. First, Saudi Arabia is said to fear that any military response could rapidly escalate and lead to further attacks against the kingdom and its vulnerable oil facilities.

Another issue is that American military forensic specialists have only arrived in the past couple of days at the site of the attacks in Saudi Arabia. Their analysis of circuit boards recovered from one of the cruise missiles — which could provide valuable clues about the missile’s trajectory and flight path — is still underway. That information could be important to making a case as to who is responsible for the attacks.

Secretary of State Mike Pompeo said Thursday that Mr. Trump was seeking a peaceful route. “We’d like a peaceful resolution indeed,” he told reporters in the United Arab Emirates before ending a two-day trip to the Gulf region. “We’re still striving to build out a coalition. I was here in an act of diplomacy while the foreign minister of Iran is threatening all-out war to fight to the last American. We’re here to build out a coalition aimed at achieving peace and a peaceful resolution.”

Mr. Pompeo said the United States planned to impose more sanctions on Iran, as Mr. Trump had announced on Wednesday. “We have set about a course of action to deny Iran the capacity and the wealth to prevent them from conducting their terror campaigns,” he said. “And you can see from the events of last week there’s more work to do.”

European nations, which have been trying to salvage the 2015 nuclear agreement with Iran, have been cautious in their response to the attack in Saudi Arabia. On Wednesday, the French government announced that President Emmanuel Macron promised in a telephone call the previous day with Crown Prince Mohammed bin Salman that French experts would go to Saudi Arabia to assist in the investigation, at the request of the Saudis.

Along with France, Germany and Britain, China and Russia also entered into the 2015 agreement with Iran. All five nations, four of which are permanent members of the United Nations Security Council, have criticized the Trump administration for withdrawing from the agreement. And China in particular has chafed at the sanctions on Iranian oil imposed by Washington.

American officials have not yet laid out the case against Iran and the recommendations they intend to present at the United Nations General Assembly meeting next week.