The intense scrutiny of Saudi Arabia and its crown prince, Mohammed bin Salman, may strain his close relationship with Jared Kushner, Mr. Trump’s son-in-law and top Middle East adviser. Mr. Kushner had been cultivating the prince’s support for an Israeli-Palestinian peace plan, but King Salman of Saudi Arabia has rejected it.

Some analysts have also questioned whether financial ties between Mr. Trump and Saudi businessmen compromise his policies.

“The unanswered questions about the extent to which Trump’s personal interests — as well as those of his family and associates, including Jared Kushner — have had an effect on the U.S. approach to Saudi Arabia makes the close Saudi ties all the more troubling,” said Jeffrey Prescott, a senior White House director on the Middle East during the Obama administration.

There are indications that the operation targeting Mr. Khashoggi was at least approved by Prince Mohammed.

American intelligence agencies have collected communications intercepts of Saudi officials discussing a plan to lure Mr. Khashoggi back to Saudi Arabia and then detain him, said a former senior American official. The official added it was inconceivable that such a plan could be carried out without the approval of the crown prince.

Turkish security officials suspect that Mr. Khashoggi was killed by a Saudi murder squad sent by the kingdom’s leadership, and that his body was dismembered with a bone saw and taken out of the building. A Turkish newspaper close to the government published names of 15 suspects who are believed to have left Turkey to return to Saudi Arabia the same day on two private planes; one is a top Saudi autopsy expert and another a lieutenant in the Royal Saudi Air Force.

Saudi leaders maintain Mr. Khashoggi left the consulate on his own.

Mr. Trump notably made Saudi Arabia a destination for his first trip abroad as president, in May 2017, during which he announced a $110 billion weapons deal with the kingdom. Not only is Mr. Trump relying on Saudi Arabia to persuade Palestinians to support a peace plan, he is also dependent on the kingdom to help contain Iranian influence in the region.