But Saudi Arabia strongly rejects he was killed inside the mission.
American lawmakers have threatened tough punitive action against the Saudis, and Germany, France and Britain jointly called for a "credible investigation".
The shares of Saudi Arabia in the Riyadh stock market plunged as much as 7 per cent on Sunday, much to the jitters of the investor.
Already, global business leaders are pulling out of the kingdom's upcoming investment forum, a high-profile event known as "Davos in the Desert", though it has no association with the World Economic Forum.
The exchange dropped by over 500 points, then clawed back some of the losses, ending the day down more than 4 per cent.
USA officials have also said that the crown prince of Saudi Arabia, Mohammed bin Salman, ordered an operation to lure Khashoggi from his home in Virginia back to Saudi Arabia and then to detain him, according to US intelligence intercepts of Saudi officials discussing the plot.
The Saudi prosecutor has received instructions "to work quickly", so an announcement could happen within days, the Saudi official said. Turkish officials say they believe Saudi agents killed and dismembered Jamal Khashoggi in Istanbul.
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Theologian Rob Lee, a descendant of the Confederate general , said he was "disheartened" to hear Trump praise his ancestor. Steve Chabot (R), the incumbent in district's Congressional race, a fact that Chabot seemed perturbed by.
The crown prince, ambitious, aggressive and just 33 in a kingdom long ruled by aging monarchs, has considerable weight in Saudi government actions.
"The Saudi economy has vital and influential roles for the global economy", the source told SPA.
The kingdom has called the allegations "baseless" but has offered no evidence the writer left the consulate.
Saudi Arabia has responded to Western statements by saying it would retaliate against any pressure or economic sanctions "with greater action", and Arab allies rallied to support it, setting up a potential showdown between Saudi Arabia and its main Western allies. The broadcaster said it wasn't immediately clear if those who arrived were Turkish or Saudi representatives.
Similar campaigns have been trending on social media in Saudi Arabia and the UAE, although there has been no official backing so far.
Saudi Arabia on Sunday warned against threats to punish it over last week's disappearance of Khashoggi, as European leaders piled on pressure.
But Riyadh vowed to hit back on October 14 against any punitive measures as its stock market tumbled, with the fallout from the crisis threatening to imperil Prince Mohammed bin Salman's much-hyped economic reform drive.
The Turkish government has also told the Trump administration that it possesses audio recordings of what occurred inside the consulate that day - evidence that US officials said supports the conclusion that Khashoggi was interrogated, tortured and then murdered.
Those policies are all seen as initiatives of the crown prince, who has also presided over a roundup of activists and businessmen.