Already, worldwide business leaders are pulling out of the kingdom's upcoming investment forum, a high-profile event known as "Davos in the Desert", and the sell-off on Riyadh's Tadawul stock exchange showed that investors are uneasy.
Turkey's state-owned Anadolu news agency said the delegation would hold talks with Turkish officials over the weekend.
Major U.S. defense contractors have expressed concern to the Trump administration that lawmakers angered by the disappearance of a Saudi journalist in Turkey will block further arms deals with Saudi Arabia, a senior U.S. official told Reuters on Friday.
Mr Khashoggi, who has been living in self-imposed exile for the past year, vanished on Oct 2 after he entered the Saudi consulate in Istanbul to obtain a document.
Saudi Arabia warned Sunday it will respond to any "threats" against it as its stock market plunged following President Donald Trump's warning of "severe punishment" over the disappearance of Washington Post contributor Jamal Khashoggi.
The king appeared to try to calm tensions between the countries, after Turkish officials accused Saudi Arabia of murdering Mr Khashoggi and dismembering his body, a claim Saudi Arabia vehemently denies.
Khashoogi, who had been living in self-imposed exile in the U.S., had been considered to be close to the Saudi royal family before becoming critical of the current government and Crown Prince Mohammed bin Salman, 33.
Big names from media and business have already cancelled appearances at a major conference in Riyadh this month and both the International Monetary Fund chief and the United States treasury secretary made their attendance conditional on the findings in the case.
Turkish and foreign media who have been camped outside the consulate all week noticed the motorcade arriving on Friday but it had not been immediately clear who the Saudi personnel entering the consulate were.
Cory Gardner, a senator from Trump's Republican Party, told reporters that arms sales would be "a huge concern" if Saudi Arabia is found responsible.
Saudi Arabia rejects the allegations in Turkey as baseless.
Branson, who dropped two directorships linked to Saudi tourism projects around the Red Sea, said claims about Khashoggi's disappearance would "change the ability of any of us in the West to do business with the Saudi government".
According to The Washington Post, the Turkish government would have informed U.S. authorities that they had video and audio recordings showing that the journalist was murdered in the consulate.
Ankara and Riyadh have worked over recent years to maintain cordial relations despite disputes on key issues, such as the ousting of the Islamist Egyptian government and the blockade on Turkey's key regional ally Qatar.
Turkish authorities have been given permission to search the consulate - Saudi sovereign territory - but it has not yet taken place.
The newspaper reported there had been intense diplomatic contacts between the two sides.
But Ankara and Riyadh disagreed over the search after Saudi officials reportedly said they would only allow a superficial "visual" search.
Turkish daily Milliyet reported "arguments and shouting" could be heard on the recordings. But Mr Khashoggi's disappearance has led several business leaders and media outlets to back out of the upcoming investment conference in Riyadh called the Future Investment Initiative.
The CEO of ride-hailing app Uber, Dara Khosrowshahi, said that he will no longer be attending the event unless "a substantially different set of facts emerges".
He said any response to Khashoggi's killing "needs to be strong, not symbolic", including the possibility of cutting off US weapons sales to Riyadh, or it would undermine the U.S.'s moral standing in the world.
Mr Khashoggi, a Saudi national living in the USA since September 2017 fearing arrest, criticised some policies of Mohammed bin Salman and Riyadh's intervention in the war in Yemen.