Khashoggi, who would have been 60 this month, sought refuge in the United States after fleeing his native Saudi Arabia after the 2017 appointment of strongman Mohammed bin Salman as heir to the throne.
Separately, the SPA also reported that Crown Prince Mohammed bin Salman bin Abdulaziz made a telephone call to Mr Salah Khashoggi, in which the prince expressed his condolences to Salah and his family on the death.
US Treasury Secretary Stephen Mnuchin said Saudi Arabia's admission that the Washington Post columnist was killed in a fistfight was a "good first step but not enough", though he added it was premature to discuss sanctions against Riyadh.
German Chancellor Angela Merkel added that Berlin would not export arms to Saudi Arabia "in the current situation".
Turkish President Recep Tayyip Erdogan announced that he will reveal details about the Turkish investigation of the alleged murder of the journalist on Tuesday.
Before Riyadh's admission, Turkish sources said a team of 15 Saudis were sent to Istanbul and killed Khashoggi, a critic of the crown prince who moved to the United States previous year and wrote for the Washington Post. Turkish sources say authorities have an audio recording purportedly documenting Khashoggi's murder.
Britain joined forces with France and Germany yesterday with a joint statement condemning the killing of journalists as unacceptable.
The man in the video, identified by the official as Mustafa al-Madani, was allegedly part of what investigators have said was a hit squad, sent to kill the journalist at the Saudi consulate during a scheduled appointment to get papers for his upcoming wedding. He also insisted that Prince Mohammed, defacto ruler of Saudi Arabia, was not to blame.
"It will not have any positive consequences if we halt arms exports but other countries at the same time fill the gap", he said.
After days of denying knowledge of his whereabouts, Saudi Arabia on Saturday claimed Khashoggi died during a fight inside the consulate.
"The world is watching", Kushner said was his advice to Prince Mohammed.
That's according to statements published early Monday by the state-run Saudi Press Agency.
But despite its ambitions, analysts say China's role in the Middle East will be limited, and it will be hard to boost ties with Riyadh while maintaining relations with Saudi rival Iran.
Turkey earlier said 15 Saudis who travelled to Istanbul were involved in Khashoggi's disappearance.
The king also ordered a restructuring of the intelligence service, to be led by Prince Mohammed, suggesting the prince still retained wide-ranging authority.
Trump said: "We'd like to find out where it is and what happened".
The kingdom has since admitted Khashoggi died in a "brawl" inside the consulate and said it has fired five top officials and arrested 18 others in an investigation into the killing.
"A lot of the reforms they've been making there to help us track down the terror financing and also to push back against the people who are perverting the religion, have been very historic over the previous year", he said.