Pompeo "also thanked the King for his commitment to supporting a thorough, transparent, and timely investigation of Khashoggi's disappearance", the statement read. There has been no evidence to substantiate Khashoggi had such ties.
Turkish crime scene investigators carried out a eight-hour search of the consulate on Monday night in an investigation to look into what happened to Khashoggi, who was last seen entering the Saudi consulate on October 2.
The search of the consulate continued into the early hours of Tuesday.
Saudi officials have repeatedly denied any knowledge of the journalist's whereabouts, but Turkish officials claim they have evidence to prove the Saudi dissident was killed while inside the consulate.
Unnamed Turkish officials say a search of the Istanbul Saudi consulate gave more evidence that he was killed there.
Trump has been more cautious in saying what could happen if the reports that the Saudi government was behind the disappearance are true. Since Mr. Khashoggi's disappearance, powerful USA executives have withdrawn from a high-profile investment conference in Riyadh this month.
Khashoggi, a familiar face on Arab talk shows, moved to the United States past year fearing retribution for his criticism of Prince Mohammed, who has cracked down on dissent with arrests.
LATEST: Turkish sources reveal details of how @JKhashoggi was murdered.
But it was delayed because no Saudi official was present for the joint investigation, the Turkish official added.
Trump previously warned of "severe punishment" for the kingdom if it was found to be involved in Khashoggi's disappearance, which has spooked investors in Saudi Arabia and SoftBank, a Japanese firm that manages tens of billions of dollars for the kingdom. Pompeo is expected to meet with Turkish authorities as well before returning to Washington this week.
CBN News Senior International Correspondent Gary Lane says, "I think he sent Pompeo there because he wants the King to know, 'Look, we're serious about this".
A search was due to be conducted on Tuesday of the consul's residence, some 200 metres away from the consulate. He later in the day left Turkey for Germany and the United States.
The G7 foreign ministers called for those responsible to be held accountable.
US Secretary of State Mike Pompeo visited Saudi Arabia on Tuesday for talks with King Salman, Crown Prince Mohammed bin Salman, and Foreign Minister Adel al-Jubeir.
"We will remain in close contact with Saudi and Turkish authorities as they complete this process and ultimately announce their findings", said Pompeo.