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.
Saudi Arabia initially said he had left the building unharmed but on Friday admitted for the first time he was dead, saying that he was killed in a fight.
While the claim has not been verified by officials in public, Turkish authorities have consistently leaked details of the investigation to pro-government media outlets and their reports have been largely accurate. "Then Prince Mohammed contacted Khashoggi by phone and tried to convince him to return to Riyadh", the report alleges. But critics believe the complex scheme that led to Khashoggi's death could not have occurred without the knowledge of Mohammed bin Salman, the country's powerful 33-year-old crown prince.
Turkish authorities believe Khashoggi's killers held him down while his fingers were hacked off and then injected him with a lethal drug before carrying him into another room where he was hoisted onto a conference table and dismembered.
They added that it was "hard to imagine what crime the Saudi government would need to commit" for it to be condemned by ministers. Saudi Arabia so far has not acknowledged or explained Mutreb's presence in Istanbul - nor that a forensics and autopsy expert was also on hand for Khashoggi's arrival at the consulate. Both areas are now being searched for Khashoggi's remains.
Saudi Arabia's admission on Friday - after weeks of denials - that Khashoggi was killed in a "fistfight" and that 18 Saudis have been detained has been met with widespread scepticism and allegations of a cover-up created to absolve Prince Mohammed of direct responsibility.
However, in the footage, Madani is wearing the same sneakers he had on prior to entering the consulate that do not match Khashoggi's outfit.
The consulate later issued a statement saying it was working with Turkish authorities "to uncover the circumstances" of his disappearance.
However, the new narrative - that Khashoggi was accidentally strangled after a brawl erupted between him and officials inside the consulate - was greeted with scepticism and condemnation from the global community.
At the same time, Saudi officials have failed to answer questions about where Khashoggi's remains are and have offered inconsistent narratives for how he was killed, undermining the government's assertion that Khashoggi died after a fistfight broke out when he was confronted by agents seeking to bring him back to Riyadh while he was visiting the Saudi Consulate in Istanbul on October 2.
Hürriyet columnist Abdulkadir Selvi wrote on October 22 that the "hit squad" in the Saudi consulate "strangulated Khashoggi in 7-8 minutes".
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The kingdom's claim on Saturday that Khashoggi died in a "fistfight" met worldwide skepticism and allegations of a cover-up to absolve the 33-year-old crown prince of direct responsibility.
He did not provide proof to substantiate the findings of the investigation and the other evidence.
"We are determined to find out all the facts and we are determined to punish those who are responsible for this murder", he said.
Asked about allegations that Mr Khashoggi had been tortured and beheaded, he said preliminary results of the investigation did not suggest that.
Turkish President Recep Tayyip Erdogan has said that on Tuesday, the same day a glitzy investment forum in Riyadh spearheaded by Prince Mohammed is to take place, that details of Khashoggi's killing "will be revealed in all its nakedness".
Saudi prosecutors said 18 people had been arrested and five top officials fired for their connection to the case.
"The Turks have been talking more to the media than they have [to] us", Corker said of the North Atlantic Treaty Organisation ally.
Turkish officials suspect Mr Khashoggi was killed inside the consulate by the team of Saudi agents and his body cut up.
Turkish news agency Anadolu Agency reported Sunday that Khashoggi's fiancee, Hatice Cengiz, has been given 24-hour police protection.
During a joint interview with Britain and France, Mrs Merkel said that she condemned the killing of Mr Khashoggi "in the strongest terms".