By Eric Schmitt, Julian E. Barnes and David D. Kirkpatrick, New York Times–

American investigators are examining missile circuit boards recovered after strikes against Saudi oil facilities to determine the trajectory of the attack — and whether it originated from Iran — as the Trump administration debates how, and whether, to retaliate.

Analysts are poring over satellite imagery of the damage sites, and assessing radar tracks of at least some of the low-flying cruise missiles that were used. Communication intercepts from before and after the attacks are being reviewed to see if they implicate Iranian officials.

Perhaps most important, forensic analysis is underway of missile and drone parts from the attack sites. The Saudis have recovered pristine circuit boards from one of the cruise missiles that fell short of its target, providing forensics specialists the possibility of tracing the missile’s point of origin, according to a senior American official briefed on the intelligence.

One theory gaining traction among American officials is that the cruise missiles were launched from Iran and programmed to fly around the northern Persian Gulf through Iraqi air space instead of directly across the gulf where the United States has much better surveillance, one senior official said. In the hours before the attacks, American intelligence detected unusual activity at military bases in southwest Iran that would be consistent with preparations for strikes, another senior American official said.

Within the administration, there is much discussion over what retaliatory action to take, if any, and whether such a response would appear to be doing the Saudis’ bidding. The question is a challenging one for President Trump, who first declared after the attacks that the United States was “locked and loaded,” but then softened his tone and said he would like to avoid conflict.

The attack is viewed as the most destructive strike to Saudi Arabia since it opened an offensive in Yemen more than four years ago. The strikes at the Abqaiq processing facility and Khurais oil field initially cut by more than 50 percent the oil produced by the kingdom, which supplies about a tenth of the worldwide total. By Tuesday, Saudi Aramco, Saudi Arabia’s national oil company, said it would fully restore oil production by the end of September at facilities that were attacked by air on Saturday.

Defense Secretary Mark T. Esper and Gen. Joseph F. Dunford Jr., the chairman of the Joint Chiefs of Staff, have presented Mr. Trump with an array of military options — presumably both bombing targets such as the missile-launching sites and storage areas as well as covert cyberoperations that could disable or disrupt Iran’s oil infrastructure.

A big concern is to ensure that any strikes be proportional and not escalate the conflict, particularly with world leaders gathering next week in New York for the United Nations General Assembly. Officials also voiced worry about the cost of doing nothing, at least openly, in response to attacks that have cut in half the oil production of one of Washington’s main allies in the Middle East.

If Iran is proved to be behind the attacks, it may be because it is looking for increased diplomatic and economic leverage, said current and former officials. Tehran has been pressed by the tough economic sanctions imposed by the Trump administration. Although an attack by Iran would represent a sharp escalation, Iranian officials may be counting that Mr. Trump’s reluctance to start a war in the Middle East will restrain the American response. Iran may believe that by committing a dramatic strike, the current and former officials said, it could improve its negotiating position before the United Nations meeting.

American officials say they have no doubt that the drones and missiles used in the attacks were Iranian technology and components. But they have not yet released information on whether the strikes were planned and directed by Iran, and launched by Iran’s proxies in the region — or whether they were actually launched from Iranian territory.

Some officials said they have come to believe the cruise missiles were launched from Iran, but others familiar with the intelligence noted that the evidence is not yet irrefutable, and Tehran has taken steps to obscure the origin of the strike.

The United States has prepared a document laying out the current understanding of the facts of the strike on Saudi Arabia in which the American government has “high confidence,” according to multiple American officials. The intelligence assessment is ready to be declassified, but it will not be released until Saudi Arabia has had a chance to make its own conclusions and release information it wants, officials said.

Secretary of State Mike Pompeo was scheduled on Wednesday to meet with officials in Saudi Arabia, a visit that could result in the release of the American report.

The rulers of Saudi Arabia appear in no rush to pinpoint the source of the attack or call for any specific response.

A Saudi military spokesman said Monday that the kingdom’s initial investigation had indicated that the weapons were Iranian-made and that the attack was not launched from Yemen. But so far the Saudis have lagged American officials in their willingness to openly blame Iran for carrying out the attack.

Underscoring its go-slow approach, the Saudi Foreign Ministry said in a statement that it intended to invite the United Nations and other international experts to visit the site of the attacks and participate in the investigations. “The kingdom will take appropriate measures based on the results of the investigation,” the statement said, suggesting that the Saudis would wait a prolonged period before taking action.

Analysts said Saudi Arabia might be reluctant to engage in a military confrontation before confirming the American response. The rulers of the kingdom may also be worried because the attack demonstrated ominous vulnerabilities in their air defense systems. Although Saudi Arabia is one of the biggest spenders in the world on military hardware, the damage from Saturday’s airstrike suggested scant preparation for a full-fledged air war.

Saudi rulers have at least once actively covered up an Iranian attack inside the kingdom to avoid making accusations that could lead to a clash. After a terrorist bombing at the Khobar Towers complex killed 19 United States Air Force personnel in 1996, scholars say, the Saudis deliberately sought to obfuscate Iran’s responsibility in an attempt to avoid a military conflict. (The United States still ultimately concluded that Iran was responsible.)

Michael J. Morell, a former acting director of the C.I.A., said during a speech on Monday night in Northern Virginia that if Iran was found responsible for directing or carrying out the attacks, that would amount to an act of war and the United States would “need to respond.”

Mr. Morell, who said he had no inside information, said he favored some kind of proportional military strike, perhaps against Iranian missile sites and storage areas but not against Iranian oil infrastructure.

Adm. Michael G. Mullen, who retired from the military after serving as chairman of the Joint Chiefs of Staff, noted the danger of the situation because there was little effective way to communicate with the Iranians to avoid escalation and misjudgment.

“It’s a situation ripe with the possibility of miscalculation,” he said. “We have not had a good line of communication with Iran since 1979, so if something happens, the odds of us getting it right are pretty small.”

Mr. Morell said it would be important to have allies such as Britain and France join any retaliation so the United States was not going it alone.

France has no evidence showing where drones that attacked the Saudi oil facilities came from, the French foreign minister said on Tuesday.

“Up to now France doesn’t have evidence to say that these drones came from one place or another, and I don’t know if anyone has evidence,” the minister, Jean-Yves Le Drian, told reporters in Cairo.

Eric Schmitt and Julian Barnes reported from Washington, and David D. Kirkpatrick from Istanbul. Helene Cooper contributed reporting from Washington, and Stanley Reed from London.