The Washington Post columnist, a strong critic of the Saudi leadership, was last seen alive entering the consulate on October 2.
Mr Pompeo meets with the Saudi Crown Prince Mohammed bin Salman in Riyadh, Saudi Arabia.
State Department spokeswoman Heather Nauert said that at the meeting, Pompeo "thanked the King for his commitment to supporting a thorough, transparent, and timely investigation of Jamal Khashoggi's disappearance".
Police searching the Saudi Consulate found evidence that Saudi writer Jamal Khashoggi was killed there, a high-level Turkish official said Tuesday, and authorities appeared ready to also search the nearby residence of the consul general after the diplomat left the country.
The kingdom has not responded to repeated requests for comment from The Associated Press. They put the president at odds with other key allies and with some leaders in his Republican Party who have condemned the Saudi leadership for what they say is an obvious role in the case. "Here we go again with, you know, you're guilty until proven innocent".
Saudi officials have called Turkish allegations that a team of 15 Saudi agents killed Khashoggi "baseless", but US media reports suggested that the kingdom may acknowledge the writer was killed at the consulate, perhaps as part of a botched interrogation.
How the crown prince, often referred to as MbS, emerges when the dust settles over Khashoggi's disappearance is a test of how the West will deal with Saudi Arabia in the future.
Jordan Henderson backs Liverpool team-mate Adam Lallana for England
Jordan Henderson will remain in Spain with the England squad despite being ruled out of their game on Monday through suspension. His drought continued in Friday night's behind-closed-doors goalless draw with Croatia in the UEFA Nations League .
"It depends whether or not the king or the crown prince knew about it, in my opinion, number one, what happened, but whether or not they knew about it". "Saudi Arabia, if you're listening, there are a lot of good people you can choose, but MBS has tainted your country and tainted himself".
The allegations that Khashoggi was killed inside the consulate have been strongly denied by Saudi Crown Prince Mohammed bin Salman and King Salman in conversations with U.S. President Donald Trump.
But there has been mounting criticism of some of the prince's moves.
On Tuesday, a Turkish Foreign Ministry official acknowledged police want to search the Saudi consul's home as well.
Khashoggi went to the consulate on October 2 to get documents for his upcoming marriage to a Turkish woman while his fiancee waited outside.
Pompeo is due to travel to Turkey on Wednesday. The Saudi Arabia kingship was said to be very unhappy with his writings and moves to unite intellectuals and activists who supported democracy.
Three others are linked by witnesses and other records to the Saudi crown prince's security detail. The claim, which was first made to the New York Times earlier in the investigation into Khashoggi's fate, comes after Turkish officials searched the consulate for nine hours on Monday night.
Meanwhile, top corporate executives including JP Morgan CEO James Dimon and Ford chairman Bill Ford pulled out of an investment conference in Riyadh following growing tension between Saudi Arabia and major powers.
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