Saudi Arabia claims the journalist then left the building but his fiancée who was waiting for him refutes this.
"We are going to try to get to the bottom of it very soon". At another point, he said, "I'm not sure yet that it exists".
"We always expected the contribution to be finalised in the [northern autumn] time frame", Brett McGurk, the State Department's envoy to the anti-Islamic State coalition, said.
"No, not at all", he declared.
The report by Yeni Safak adds to the ever-increasing pressure on Saudi Arabia to explain what happened to Khashoggi, who vanished October 2 while visiting the consulate to pick up paperwork he needed to get married.
Turkish pro-government newspaper Yeni Safak published on Wednesday what it said were details from audio recordings purportedly documenting Khashoggi's torture and interrogation.
"I do think it's important that everyone keep in their mind that we have lots of important relationships - financial relationships between USA and Saudi companies, governmental relationships, things we work on together all across the world, the efforts to" counter Iran, Pompeo said to reporters in Brussels.
"No not at all, I just want to find out what's happening", he told journalists in the White House.
"We will probably know that by the end of the week", Trump said. I don't like that.
Adding to embarrassment for the petro-state's royals, International Monetary Fund chief Christine Lagarde became the latest to pull out of Prince Mohammed's much-trumpeted investment conference next week.
The Times said it confirmed at least nine of the 15 worked for the Saudi security services, military or other government ministries.
In the column, Khashoggi discussed the results of the 2018 "Freedom in the World" report and said he "came to a grave realization" that Tunisia was the "one country in the Arab world that has been classified as 'free.'" Three other countries were given "partly free" status, while the remaining were labeled as "not free", he said.
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Jamal Khashoggi: Turkey requests Saudi consulate search
But they appear in jeopardy by the suggestion of a carefully plotted murder of a Saudi government critic, Jamal Khashoggi . Trump visited Saudi Arabia on his first worldwide trip as president and announced $110 billion in proposed arms sales.
Trump was defensive this week about the suggestion that his administration is trying to give the Saudis room to come up with a statement absolving Mohammed. The president told AP on Tuesday that that description was informed by his "feeling" from his conversation with Salman and that the king did not use the term.
The US has asked Turkey for a recording said to provide strong evidence that missing Saudi journalist Jamal Khashoggi was killed at the Saudi consulate in Istanbul.
Pompeo arrived in Ankara, the Turkish capital, on Wednesday after visiting Saudi King Salman and his son, Crown Prince Mohammed bin Salman, the day before.
And Trump ally Senator Marco Rubio (Republican-Florida) called the situation a "catastrophe" for the Saudis that will "alter the relationship between the United States and Saudi Arabia for the foreseeable future".
Earlier, Pompeo said that when he met with Saudi leaders, they did not want to talk about any of the facts involving Khashoggi's disappearance.
In the meantime, there were signs at home that Trump's party was growing uncomfortable with his willingness to defend the Saudis. "He had this guy murdered in the consulate in Turkey and you expect me to ignore it?" Lindsey Graham (R-SC), for example, who called for Mohammad bin Salman's removal from power on Fox News Tuesday.
Prince Mohammed has painted himself as the face of a new, vibrant Saudi Arabia, diversifying its economy away from reliance on oil and making some social changes.
Global leaders and business executives are severing or rethinking ties to the Saudi government after Khashoggi's high-profile disappearance.
Almutawakel runs the best-known human rights organization in Yemen, where a US -backed coalition led by Saudi Arabia has been battling an Iran-linked rebel group since 2015.
He said it was too early to say whether he endorsed other countries' actions.
Pompeo said Erdogan "made clear that the Saudis had cooperated with the investigation that the Turks are engaged in and they are going to share information".