Turkey and the United States on Thursday ratcheted up the pressure on Saudi Arabia to explain how a journalist vanished after entering its Istanbul consulate last week, with President Recep Tayyip Erdogan urging the release of CCTV footage from the mission.

The Washington Post, which Jamal Khashoggi wrote for, added to the still unresolved mystery by reporting Saudi Crown Prince Mohamed bin Salman had ordered an operation to "lure" the critical journalist back home.

Also on Thursday, a Turkish official said a Turkish-Saudi joint team will begin an investigation into the disappearance of Khashoggi.

Meanwhile, Saudi Arabia's ambassador to the United States headed back to Riyadh on Thursday and a State Department spokeswoman said the US government expects him to provide information on the disappearance of the journalist when he returns to Washington.

Khashoggi, a Saudi national whose articles have criticised the crown prince, has not been seen since October 2 when he went to the consulate in Istanbul to obtain official documents for his upcoming marriage.

Turkish officials have said he was killed - reportedly by a 15-man "assassination team" that arrived on two planes - but Riyadh denies that.

The disappearance has captured international headlines and threatens to harm Saudi's relations with both Ankara and Washington, as well as damage efforts by Prince Mohamed to improve the country's image.

Erdogan challenged Saudi Arabia to provide CCTV images to back up its account that Khashoggi had left the consulate safely, indicating he did not find the current Saudi explanations sufficient.

"Is it possible there were no camera systems in a consulate, in an embassy?" he asked.

"If a bird flew, or a fly or a mosquito appeared, the systems would capture this; they (Saudi Arabia) have the most cutting-edge systems," he was quoted as saying.

The consulate said CCTV cameras were not working that day and dismissed the murder claims as "baseless".

The case is also threatening the strong relationship the Trump administration has built with Prince Mohamed.

In a reversal from Washington's initial low-key response, President Donald Trump expressed determination to get to the bottom of the matter.

"We can't let it happen. And we're being very tough and we have investigators over there and we're working with Turkey and frankly we're working with Saudi Arabia," Trump said in an interview with "Fox and Friends".

However, a Turkish diplomatic source quoted by the state-run Anadolu news agency denied US investigators had been tasked to work on the case.

And Trump later said the United States was not limiting arms sales to Saudi Arabia over the case.

"They're going to take that money and spend it in Russia or China or someplace else," he said.

Jeremy Hunt, the foreign secretary of key Saudi ally and trade partner, Britain, said there would be "serious consequences" if the allegations were true.

Saudi Arabia also dropped a bid to join the world's club of French-speaking countries, the International Organisation of the Francophonie (OIF).

Khashoggi is a former government adviser who fled Saudi Arabia in September 2017 and lived in the US fearing arrest back home.

In his columns for the Washington Post and comments elsewhere, he was critical of some policies of Mohamed bin Salman as well as Riyadh's role in the war in Yemen.

While unnamed Turkish officials quoted in the media have been giving sometimes macabre details of the alleged murder, Erdogan has so far been more circumspect.

Erdogan said it would "not be right" to comment yet but said he had "concerns".

"It's not possible for us to stay silent regarding an incident like this," he said.

Human Rights Watch urged Prince Mohamed to "release all evidence and information" concerning Khashoggi's status.

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