Pompeo was dispatched by President Trump on Monday to meet with leaders in both countries.
Crime-scene technicians wore white coveralls, gloves and shoe covers entering the residence.
On October 6 a government source says Turkish police believe Khashoggi was murdered inside the consulate.
The rights group Prisoners of Conscience, which is an independent non-governmental organization advocating human rights in Saudi Arabia, announced in a post on its official Twitter page that it did not dismiss the possibility that Khashoggi's sudden disappearance was an attempt to silence the writer.
In Turkey on Tuesday, a high-level Turkish official told the AP that police investigators searching the Saudi Consulate had found evidence that Khashoggi was killed there.
"Here we go again with you're guilty until proven innocent", Trump told The Associated Press as he compared the allegations against Saudi Arabia to the sexual misconduct allegations from multiple women against Supreme Court Justice Brett Kavanaugh during his confirmation hearing.
Dispatched by Trump to address the crisis, Pompeo visited Riyadh on Tuesday for talks with Saudi King Salman and his Crown Prince on a visit to Riyadh. Mr. Khashoggi had fled the country a year ago amid the rise of Prince Mohammed, whom he wrote critically about in the Post.
Several US media outlets said Monday that the Saudis are preparing a report that Khashoggi's death resulted from a botched interrogation.
Inquiries are continuing into the disappearance
Asked if the United States would be willing to walk away from Saudi Arabia, Trump said: "I do not want to do that and frankly they have a tremendous order, $110 billion", referring to a promised USA arms sales to the kingdom.
"The timing of this is no coincidence", an American official involved in Syria policy said on condition of anonymity.President Donald Trump, who initially came out hard on the Saudis over the disappearance but since has backed off, said Wednesday that the USA wanted Turkey to turn over any audio or video recording it had of Khashoggi's alleged killing "if it exists".
A search expected on Tuesday at the consul's residence did not take place as family members were still present but should go ahead on Wednesday, Foreign Minister Mevlut Cavusoglu said.
"And frankly they have a tremendous order, $110 billion", he said, referring to a promised U.S. arms sales to the Saudis.
Turkish officials have said he was murdered, and the Turkish newspaper's report said an audio recording revealed gory details about Khashoggi's demise inside the Saudi Consulate in Istanbul. But Saudi Arabia strongly rejects he was killed inside the mission.
He also said 'there is a serious commitment to determine all the facts and ensure accountability, including accountability for Saudi Arabia's senior leaders or senior officials'.
He said: "No, not at all, I just want to find out what's happening".
Saudi Arabia, which denies any involvement in the kidnapping or killing of Khashoggi, has set up a joint team to investigate the disappearance with Turkey.