An anonymous Saudi official claimed the hit squad threatened him with kidnapping – but accidentally killed him in a chokehold when he resisted.
The official said: "They tried to prevent him from shouting but he died. The intention was not to kill him."
The team then rolled up the body and took it to a "local cooperator" for disposal.
Forensic teams are hunting for the body of the murdered 59-year-old journalist in woodland outside Istanbul, with officials insisting: "We'll find out what happened to the body before long".
The latest claim comes as CCTV images have emerged that could show Khashoggi's body being moved in a van.
There are also suggestions that a fleet of vans leaving the consulate were trying to avoid being tracked.
Khashoggi was last seen entering the diplomatic mission in Istanbul on October 2 but has not been seen since.
"Turkey will reveal whatever had happened," said Omer Celik of Turkey's ruling AKP party, according to Anadolu news agency.
"Nobody should ever doubt about it. We are not accusing anyone in advance but we don't accept anything to remain covered [up]."
'WE'RE INCHING OUR WAY THERE': Donald Trump speaks out on murdered journalist case
President Donald Trump says he needs to learn more about the killing of a Saudi journalist and will be working with Congress on the U.S. response.
Speaking late Saturday after a campaign rally in Nevada, he said he will be talking to Saudi Crown Prince Mohammed bin Salman soon.
Saudi authorities announced that Jamal Khashoggi, a Washington Post columnist, died in the Saudi Consulate in Istanbul after a fistfight with officials there. That explanation has sparked allegations of a cover-up intended to shield the powerful crown prince.
Trump initially said he believed the Saudi account, but on Saturday he said he still does not know where Khashoggi's body is.
Trump said: "We'd like to find out where it is and what happened… And I think we're inching our way there."
State TV in Saudi Arabia reported that two senior officials had been fired and 18 Saudi nationals arrested after a preliminary probe into the writer's death, according to state TV.
The statement from the Saudi public prosecutor added that Royal court adviser Saud al-Qahtani and deputy intelligence chief Ahmed Asiri have been sacked from their positions.
Saudi Arabia's state-run news agency also reported that King Salman now has a proposal on the "urgent need" to restructure the kingdom's intelligence services.
It's the first time since the journalist went missing more than two weeks ago that the Saudis admitted to his death.
Turkish investigators had previously stated that Mr Khashoggi was cut up with a bone saw while still alive in a horrific seven-minute execution.
The Washington Post columnist visited the consulate for paperwork required to marry his Turkish fiance and was pictured entering the building.
His fiance, Hatice Cengiz, tweeted following the Saudi announcements: "God have mercy on you my love Jamal, and may you rest in Paradise."
White House press secretary Sarah Huckabee Sanders said the US will closely follow international investigations into Khashoggi's death and will advocate for justice that is "timely, transparent and in accordance with all due process."
Donald Trump meanwhile called the Saudi explanation "credible" and insisted rulers of the Arab kingdom had not lied to him when denying prior knowledge of what happened.
He said he hoped to protect a $110bn arms deal with the Gulf state which he claimed "means 600,000 jobs".
Saudi Arabia's crown prince claims to have had no knowledge of the specific operation that resulted in his death, a Saudi official familiar with the investigation said.
The official, who wasn't named, said: "There were no orders for them to kill him or even specifically kidnap him," adding that there was a standing order to bring critics of the kingdom back to the country.
Using the initials of Crown Prince Mohammed bin Salman, they said: "MbS had no knowledge of this specific operation and certainly did not order a kidnapping or murder of anybody.
"He will have been aware of the general instruction to tell people to come back."
The official said the whereabouts of Khashoggi's body were unclear after being handed over to a "local cooperator" but there was no sign of it at the consulate.
Saudi's attorney general said in a statement: "Preliminary investigations conducted by the Public Prosecution showed that the suspects had travelled to Istanbul to meet with the citizen Jamal Khashoggi as there were indications of the possibility of his returning back to the country.
"Discussions took place with the citizen Jamal Khashoggi during his presence in the consulate of the kingdom in Istanbul by the suspects (that) did not go as required and developed in a negative way, leading to a fistfight.
"The brawl led to his death and their attempt to conceal and hide what happened."
There's been no indication Khashoggi had any immediate plans to return to the kingdom.
The Saudi statements did not identify the 18 Saudis being held by authorities and did not explain how so many people could have been involved in a fistfight.
The statement also did not shed any light on what happened to Khashoggi's body after his death.
It concluded: "The kingdom expresses its deep regret at the painful developments that have taken place and stresses the commitment of the authorities in the kingdom to bring the facts to the public opinion, to hold all those involved accountable and bring them to justice."
It comes as reports claiming the suspected hit squad behind the killing came to Britain during the Saudi crown prince's state visit.
Mohammed bin Salman was given the red carpet treatment during a three-day visit in March during which he met the Queen and Theresa May despite widespread protests over the Gulf state's human rights record.
At least three of the suspects, First Lieutenant Dhaar Ghalib Dhaar Al-Harbi, Sergeant Major Walid Abdullah Al-Shihri and Abdul Aziz Muhammad Musa Al-Hawsawi, were part of the crown prince's entourage, the news site Middle East Eye reported.
Another suspect, Major General Mahir Abdul Aziz Muhammad Mutrib, was seen emerging from a car in Downing Street during the visit, according to the Daily Mail.
Jeremy Hunt had earlier warned there will be "consequences" for the UK's relationship with Saudi Arabia if it was found the journalist was murdered.
The Foreign Secretary said the Government remained "extremely concerned" about his fate after he went missing when he visited the consulate more than two weeks ago to get paperwork so he could marry.
His warning came as former MI6 chief Sir John Sawers said "all the evidence" suggested that Mr Khashoggi had been murdered on the orders of someone close to the crown prince.
Turkish government sources have alleged Mr Khashoggi, a critic of the prince and the Saudi government, was tortured and murdered and by a hit squad flown in from Riyadh.
The Saudis first dismissed the claims as baseless, without providing an explanation as to how he disappeared after entering the consulate.
On Thursday, Donald Trump threatened to punish the Saudi royals after he finally admitted the Washington Post journalist is likely to be dead.
Khashoggi was reportedly chopped into pieces while still alive in a horrifying seven-minute execution – and his murderers listened to music on their headphones while surgically dismembering his body.
A source claims to have heard a recording from the writer's Apple Watch capturing the moment he was allegedly dragged into a study and butchered.
The anonymous source said Khashoggi – a Saudi journalist based in the US – can be heard screaming as he's dragged from the Consul General’s office to a desk in next door study.
They claim the consul was taken out of the room before Khashoggi was "injected with an unknown drug".
The source told the Middle East Eye: "There was no attempt to interrogate him. They had come to kill him."
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