Turkish intelligence officials chose to review an audio-visual feed from inside the Saudi consulate - a feed whose existence Ankara has not publicly acknowledged, sources told CNN.
In his brief comments to reporters, Pompeo also stressed the "longstanding strategic relationship" between the USA and Saudi Arabia.
Turkish sources have told Reuters the authorities have an audio recording indicating Khashoggi, a USA resident who wrote columns for the Washington Post, was killed.
But Pompeo, "who smiled broadly as he greeted Crown Prince Mohammed bin Salman, appeared less intent on determining the truth than in helping the de facto Saudi ruler escape from the crisis he triggered", said the Post.
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"Khashoggi was tied to the Muslim Brotherhood", Fox News anchor Harris Faulkner said Thursday on the show "Outnumbered".
A report by the Washington Post - for which Khashoggi was a contributor - said Thursday that Trump-allied House Republicans are digging up right-wing dirt on the journalist in an effort to somehow lessen the significance of his death for US foreign policy.
On Wednesday, German Foreign Minister Heiko Maas said he was postponing a planned trip to Saudi Arabia pending the outcome of the investigation into Khashoggi's disappearance, calling the case "extremely worrying. and disturbing".
"I told the president this morning that we ought to give them a few more days", Pompeo told reporters. Turkish police are searching a forest on the outskirts of Istanbul and a city near the Sea of Marmara for the remains of Khashoggi more than two weeks after he vanished after entering the Saudi consulate in Istanbul, two senior Turkish officials told Reuters. And a senior USA official said Pompeo had warned the Saudi crown prince that his credibility as a future leader was at stake, reflecting the administration's concern about how the case could affect relations.
"I told President Trump this morning that we ought to give them a few more days to complete that so we can get a complete understanding the facts surrounding that", Pompeo told reporters after meeting Trump, before "we can make a decision about how the United States should respond".
Turkey's pro-government press has reported that Turkey has an audio recording that proves the alleged murder of Khashoggi at the consulate and that he was tortured before his death. Authorities have not said specifically what they found, although technicians carried out bags and boxes from the consul general's home.
The official, who was not authorized to publicly discuss details of the private meetings and spoke on condition of anonymity, said Pompeo told the crown prince that "time is short".