The newspaper, for which Khashoggi is a columnist, cited anonymous officials as saying the recordings show a Saudi security team detained the writer when he went to the consulate on Oct. 2 to pick up a document for his upcoming wedding.
A delegation from Saudi Arabia arrived in Turkey Friday as part of an investigation into the writer's disappearance.
Saudi Arabia has called the allegation it abducted or harmed Khashoggi "baseless." However, it has offered no evidence to support its claim he left the consulate and vanished despite his fiancée waiting outside.
The 59-year-old journalist, who was considered close to the Saudi royal family, had become a critic of the current government and Crown Prince Mohammed bin Salman, the 33-year-old heir apparent who has introduced reforms but shown little tolerance for criticism.
US President Donald Trump said on Thursday that he saw no reason to cut off arms sales to Saudi Arabia because of the disappearance of Khashoggi, possibly setting up a clash with the US Congress.
Trump also said the United States may be closer to finding out what happened to Khashoggi, a prominent critic of Saudi policies who was last seen entering the Saudi consulate in Istanbul on Oct. 2.
Speaking to reporters, Trump said he saw no reason to block Saudi purchases of US arms or its investments in the United States despite the journalist's case, saying the Arab kingdom would just move its money into Russia and China.
"They're spending $110 billion on military equipment and on things that create jobs ... for this country. I don't like the concept of stopping an investment of $110 billion into the United States, because you know what they're going to do? They're going to take that money and spend it in Russia or China or someplace else," he said.
His comments prompted pushback from members of the US Senate, including from some of his fellow Republicans, many of whom signed a letter on Wednesday forcing his administration to investigate Khashoggi's disappearance and paving the way to possible sanctions on Saudi officials.
"If it's found that they murdered a journalist, that will hugely change our relationship," Senator Bob Corker, chairman of the Senate Foreign Relations Committee, told reporters. "There will have to be significant sanctions placed at the highest levels."
The Khashoggi incident might make it very hard for the Trump administration to win congressional approval for arms sales to the Saudis. Many lawmakers, including some Republicans, have already questioned US support for Saudi's involvement in Yemen's war, which has prompted a humanitarian crisis.
Under US law, major foreign sales of military equipment can be blocked by Congress. There is also an informal process in which key lawmakers can put "holds" on arm sales.
British billionaire Richard Branson said his Virgin Group would suspend its discussions with Saudi Arabia's Public Investment Fund over a planned $1 billion investment in the group's space ventures, while a number of media companies pulled out a planned Saudi investment conference.
The New York Times said it would no longer be a sponsor of the Future Investment Initiative conference in Riyadh. Economist Editor-In-Chief Zanny Minton Beddoes and CNBC anchor and New York Times journalist Andrew Ross Sorkin both decided they would no longer attend.