For weeks, the Saudi royal authorities insisted that Mr. Khashoggi had left the Istanbul consulate the same day he visited. It was only this past Saturday that the Saudi authorities admitted he had been killed inside the building, describing it as an accident. They said 18 Saudis suspected of involvement had been detained in Saudi Arabia.

Turkish officials have said they have evidence including audio recordings that a team of Saudi assassins killed Mr. Khashoggi within minutes of his entry to the consulate, dismembered his body and then tried to cover up his death — even creating a fictitious trail by having a Saudi agent who resembled Mr. Khashoggi walk out of the consulate wearing the victim’s clothes.

President Trump, a close ally of the Saudi royal family, has said he is skeptical of the Saudi explanations for what happened and has called the cover-up “one of the worst.”

In an interview with The Wall Street Journal on Tuesday, Mr. Trump said that ties between the United States and Saudi Arabia would be damaged if the crown prince had been dishonest with him. “Certainly it would be a very bad thing in terms of relationship,” the president said. “It would take a while to rebuild.”

Mr. Trump’s Central Intelligence Agency director, Gina Haspel, has been in Turkey for the past few days to get more information from her Turkish counterparts.

The Sabah, a pro-government Turkish newspaper, reported that Turkish officials had shared evidence including audio recordings with Ms. Haspel. American intelligence officials would not comment on Ms. Haspel’s meeting.

For the recordings to have real usefulness to the C.I.A. or other agencies, the Turks would have to provide a full copy so American intelligence operatives can perform technical analysis and establish their authenticity. But even then, the recordings would most likely be of little value on the key policy question: whether the Saudi crown prince was connected to the killing, officials briefed on the intelligence said.