The Sabah newspaper, which is close to President Recep Tayyip Erdogan, identified the team members, including several alleged security officials, and published photos of each of them, apparently taken at passport control.
Kaye spoke to The Associated Press moments after he and two colleagues called for an global, independent investigation into the disappearance of Khashoggi at the Saudi consulate in Istanbul.
The video then cuts away to traffic outside the Saudi Consulate in Istanbul's upscale 4th Levent neighborhood, showing vehicles with green diplomatic license plates.
CCTV footage showed Khashoggi entering the consulate - but there is no public evidence that he either left or was kidnapped or killed.
Turkish police were looking into two private aircraft that landed at Istanbul's Ataturk airport on October 2 at different times carrying the individuals of interest in the case.
He first visited the Saudi consulate in Istanbul on 28 September to obtain a document certifying that he had divorced his ex-wife, but he was told he would have to return.
The newspaper also claimed that Turkish employees at the residence were "hastily" told to take a vacation on the day Khashoggi went missing.
The Washington Post is reporting that before the journalist disappeared on October 2, Saudi officials discussed a plan to lure Khashoggi back to Saudi Arabia.
The release of the photographs and video raises pressure on Saudi Arabia after Khashoggi disappeared October 2 during a visit to the consulate.
Khashoggi, a former Saudi government adviser, had been living in self-imposed exile in the United States since past year fearing possible arrest.
A string of reports on Tuesday added new, shocking details to the disappearance of journalist and dissident Jamal Khashoggi, including accounts of Saudi agents wielding a bone saw and a plea from his fiancée that he be returned home.
Beyond that, conjecture and anonymous security sources paint a picture of possible abduction and even murder, with the Saudi consulate in Istanbul at the centre of a mystery that has captured the global media's attention.
Sabah daily on Wednesday published the names and images of what it called the "assassination team" including a man called Salah Muhammed Al-Tubaigy whose name it said matched that of a lieutenant-colonel in the Saudi forensic department.
He has been critical of some policies of the Saudi Crown Prince Mohammed bin Salman and Riyadh's intervention in the war in Yemen.
On Wednesday, the Post published a column by Khashoggi's fiancée, Hatice Cengiz.
Signs of such a challenge began to emerge Monday night when Secretary of State Mike Pompeo called on the Saudis to "support a thorough investigation of Mr. Khashoggi's disappearance and to be transparent about the results of that investigation".
The private jets flew out of Istanbul - with one going to Egypt and the other to Dubai. Saudi officials haven't acknowledged that.
A total of 25 to 30 professional and non-professional journalists are now believed to be detained in Saudi Arabia, which is ranked 169th out of 180 countries in RSF's 2018 World Press Freedom Index, the organisation also said.
The Turkish foreign ministry on Tuesday said Saudi authorities gave them the greenlight to search the consulate but it has not yet taken place.
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