Saudi Arabia had earlier denied killing Khashoggi and denounced such assertions as "lies", saying he left the building shortly after entering.
The Wall Street Journal, citing a Turkish official who has heard the recording, said Mr Khashoggi was allegedly killed and dismembered in the office of the Saudi consul general, Mohammad al-Otaibi, who was in the room at the time.
"The president is willingly and knowingly doing the counter messaging for the Saudi kingdom", noted Washington Post national security reporter Greg Miller in a tweet on Tuesday.
A second search, cancelled on Tuesday because Saudi officials were not able to join, is expected to happen later on Wednesday.
Saudi Arabia is considering an admission that journalist Jamal Khashoggi died during an interrogation that went wrong, U.S. media reported yesterday. "Who knows?" the president said, describing the situation as "terrible".
Pompeo will hold talks in Turkey on Wednesday, the Turkish foreign ministry said, after his visit to Riyadh.
A Saudi contribution of $100 million to USA -backed stabilization efforts in Syria arrived in American accounts Tuesday, just as State Mike Pompeo touched down in Riyadh to discuss the missing Saudi journalist, an anonymous US official told The New York Times.
That leaves Trump, who Monday suggested it might have been "rogue killers" behind Khashoggi's murder, out of step with even close allies in Washington like U.S. Sen.
"Saudis claimed that his [consul's] family was inside", said Mevlut Cavusoglu addressing members of the media following his meeting with U.S. Secretary of State Mike Pompeo in Ankara.
"I heard that [CNN] report, but nobody knows if it's an official report", he said in Georgia.
Turkish investigators searched the consulate for the first time on Monday night, gathering "strong" but inconclusive evidence that Khashoggi was killed there.
"The king has ordered the public prosecutor to open an internal investigation into the Khashoggi matter based on the information from the joint team in Istanbul", an official quoted by Reuters news agency said.
"My assessment from these meetings is that there is a serious commitment to determine all the facts and ensure accountability, including accountability for Saudi Arabia's senior leaders or senior officials", Pompeo said in a statement.
While Pompeo was in his meetings in Saudi Arabia, Trump, in Washington, said on Twitter, "For the record, I have no financial interests in Saudi Arabia (or Russian Federation, for that matter)".
The newspaper said one of the Saudi "torturers" replied: "Shut up if you want to live when you return to (Saudi) Arabia".
"We just went through that with Justice Kavanaugh and he was innocent all the way as far as I'm concerned", Trump told the AP.