Trump, who dispatched Pompeo to speak to the monarch over Khashoggi's disappearance, said after talking with King Salman that the slaying could have been carried out by "rogue killers".
The three posed for photos before their meetings, but said nothing in front of journalists.
Pompeo had just come from Riyadh, where he spoke Tuesday with Saudi King Salman and Crown Prince Mohammed bin Salman.
Turkish authorities have told US officials that they have recordings from inside the Saudi consulate in Istanbul that provide evidence that the missing journalist was killed inside.
Previously, a source familiar with the ongoing investigation told CNN that Turkish authorities have audio and visual evidence that showed Khashoggi was killed inside the Saudi consulate.
Turkish investigators were expanding their search to include the Saudi consul's residence in Istanbul and consulate vehicles, Foreign Minister Mevlut Cavusoglu said on Tuesday.
The Turkish inspection team included a prosecutor, a deputy prosecutor, anti-terror police and forensic experts, the state-run Anadolu news agency reported. They suspected Khashoggi of having ties to the kingdom's arch rival, Qatar, the source said.
Turkey has wanted to search the consulate for days. Turkish officials fear he was killed and dismembered.
The White House previously brushed aside threats by Saudi Arabia that it may economically retaliate for any US punitive action imposed over the suspected murder of Khashoggi, pledging a "swift, open, transparent investigation" into his disappearance.
Graham said he will never return to Saudi Arabia until 33-year-old bin Salman, nicknamed MBS, is out of power.More news: Native American Rep. Blasts Liz Warren's Claim to Shared Heritage: 'It’s Disgusting'
A fourth suspect traveled with a passport with the same name of another member of the Saudi royal guard, Muhammed Saad Alzahrani, the report said citing a name search in a popular app in Saudi Arabia called "Menom3ay".
Security services in Turkey have used pro-government media to leak details of Khashoggi's case, adding to the pressure on the kingdom.
US Secretary of State Mike Pompeo has been meeting King Salman in Riyadh.
Khashhoggi's disappearance has created a flurry of criticism against Saudi Arabia and the Crown Prince Mohammed bin Salman, who was seen by some as a populist reformer. "I spoke to the king yesterday, the crown prince, today wanting to know what was going on, what was happening, and he said very strongly that he and his father knew nothing about it".
A report by CNN quoted two sources as saying that the Saudi side is preparing a report to acknowledge that the interrogation of Khashoggi had been meant to abduct him from Turkey, but went wrong and lead to his death.
On Tuesday, Freeland joined G7 foreign ministers in affirming freedom of the press and calling on Saudi Arabia to conduct a thorough and transparent investigation into the disappearance of journalist Jamal Khashoggi.
"The effort behind the scenes is focused on avoiding a diplomatic crisis between the two countries", said Ayham Kamel, the head of the Eurasia Group's Mideast and North African practice.
Pompeo said: "They made a commitment to hold anyone connected to any wrongdoing that may be found accountable for that, whether they are a senior officer or official".
Khashoggi vanished October 2 on a visit to the Saudi Consulate in Istanbul.
"In view of the seriousness of the situation surrounding the disappearance of Khashoggi, I believe the inviolability or immunity of the relevant premises and officials bestowed by treaties such as the 1963 Vienna Convention on Consular Relations should be waived immediately", Bachelet said.