Secretary of State Mike Pompeo on Wednesday refused to blame key US ally Saudi Arabia over the disappearance of journalist Jamal Khashoggi even as Riyadh faced new claims he was killed and tortured inside its Istanbul consulate.

After talks with the Saudi leadership in Riyadh marked by expressions of mutual goodwill, Pompeo in Ankara met President Recep Tayyip Erdogan whose government also remains wary of giving public details about Khashoggi's fate.

Pro-government Turkish media published gruesome new allegations Khashoggi was killed by being gradually dismembered by a Saudi assassination squad, some of whom the New York Times said were tied to Crown Prince Mohammed bin Salman.

But Pompeo declared he did not want "to talk about any of the facts", while President Donald Trump said innocence must be presumed, drawing a parallel with his US Supreme Court judge nominee who faced sexual assault accusations.

The controversy has blown a massive hole in attempts by Prince Mohammed to promote himself as a modern reformer and led to a spate of cancellations from a major Riyadh investment conference scheduled next week.

Khashoggi, a former regime insider who became critical of Prince Mohammed, has not been seen since he stepped inside the Saudi consulate in Istanbul on October 2 to sort out marriage paperwork.

Turkish police on Wednesday began searching the residence of the Saudi consul in Istanbul for their investigation, with forensics experts in white overalls entering the building, an AFP correspondent said.

The Saudi consul Mohammed al-Otaibi left Istanbul for Riyadh on a scheduled Saudia flight Tuesday afternoon, with Ankara insisting he had not been expelled and left by his own choice.

Turkish police on Monday night also undertook an eight-hour search at the consulate itself, taking away soil and DNA samples. Erdogan said toxic material was found which had been "painted over".

'Complete investigation'

Pompeo came to Ankara after Riyadh where he held a 20-minute talk with King Salman and then a brief meeting and much lengthier dinner with his son Prince Mohammed.

The top US diplomat said that in Saudi Arabia he stressed the "importance of them conducting a complete investigation into the disappearance" and Riyadh had vowed to do this.

"They made a commitment that they would show the entire world the results of their investigation," said Pompeo, adding Saudi also vowed that no-one would have immunity.

But he refused to be drawn on whether Khashoggi was alive or dead and who could be responsible. "I don't want to talk about any of the facts. They didn't want to either."

Pompeo held 40 minutes of talks at the airport with Erdogan, whose government has echoed the American reticence to disclose details or make accusations.

Interviewed by state-run Anadolu news agency, Turkish Interior Minister Suleyman Soylu refused to be drawn into commenting on what may have happened inside the consulate.

"I have my own opinions... I have strong opinions but that (the investigation) is the job of the judiciary," he said. Cavusoglu also said after meeting Pompeo that the investigation had to be left to prosecutors.

Trump also refused to accuse Saudi Arabia, drawing a parallel with the case of new US Supreme Court Justice Brett Kavanaugh who had faced a swirl of allegations of sexual assault.

"Here we go again with, you know, you're guilty until proven innocent," he said. "I don't like that. We just went through that with Justice Kavanaugh and he was innocent all the way as far as I'm concerned," he told the Associated Press.

'Getting me into trouble'

Several US media said Monday that the Saudis are preparing a report that Khashoggi's death resulted from a botched interrogation. However there has yet to be any sign of this being published.

Pro-government Turkish daily Yeni Safak reported it had heard audio recordings of Khashoggi being tortured during an interrogation, having his fingers cut off and then decapitated.

It said al-Otaibi can be heard on one tape saying during Khashoggi's torture: "Do this outside. You are going to get me in trouble."

The daily reported that in another tape, an unknown individual tells Otaibi: "If you want to live when you return to Saudi Arabia, be quiet!"

The New York Times reported Tuesday that a suspect identified by Turkey was a frequent companion of the prince's. Three other suspects are linked to his security detail and a fifth is a high-level forensic doctor, the Times said.

International Monetary Fund chief Christine Lagarde was the latest to pull out of Prince Mohammed's much-trumpeted investment conference next week. An IMF spokesman said she had postponed her planned trip to the Middle East with a stop in Saudi Arabia.