"The individuals who did this did this outside the scope of their authority," he added. "There obviously was a tremendous mistake made, and what compounded the mistake was the attempt to try to cover up."
He said that Saudi Arabia did not know where the body was.
Mr Jubeir insisted that the action had not been ordered by the crown prince.
However, Yeni Safak, a media outlet close to Turkey's government, said it had information showing that the office of the crown prince received four phone calls from the consulate after the killing.
Reuters news agency reported on Sunday it had spoken to a Saudi official who said Khashoggi had died in a chokehold after resisting attempts to return him to Saudi Arabia. His body was then rolled in a rug and given to a local "co-operator" to dispose of.
A Saudi operative then reportedly donned Khashoggi's clothes and left the consulate.
CNN quoted a senior Turkish official as saying a Saudi agent had been captured on surveillance footage dressed as the journalist.
The video appears to show the man leaving the consulate by the back door on the day the journalist was killed, wearing Khashoggi's clothes, a fake beard and glasses, CNN said.
In another development, Turkish police found a car belonging to the Saudi consulate left in an underground car park in Istanbul.
Turkish media also posted footage apparently showing Saudi consular staff in Istanbul burning documents a day after Khashoggi's disappearance.
Turkey's 'full account' vow
Analysis by BBC security correspondent Frank Gardner
After weeks of calculated and often lurid leaks to the Turkish media, Tuesday morning's statement by President Erdogan is eagerly awaited.
Turkey has promised "a full account" of what happened to Khashoggi, with nothing held back.
So that would include the widely reported audio tape from inside the Saudi consulate then? And evidence of the "bone saw" allegedly brought in by the hit team that killed him?
Because both of these elements are crucial in establishing the facts about what happened and the motives of his murderers. If evidence of the bone saw can be produced then it would certainly imply murderous intent by the hit team from Riyadh.
The audio tape of his murder - if it does exist - could be excruciating to listen to - but is an essential part of the puzzle of how Khashoggi died. But Turkey, a country that has itself jailed more journalists than any other nation on Earth, may have its own reasons for holding back on what it has.
For the full story, we may have to wait a little longer yet.
How have other world leaders reacted?
Many of them have condemned the murder and demanded a full investigation:
German Chancellor Angela Merkel said "it must be cleared up", otherwise there would be no arms exports to Saudi Arabia
UK Foreign Secretary Jeremy Hunt condemned the killing "in the strongest possible terms"
French Foreign Minister Jean-Yves Le Drian said the murder was a grave crime
Canadian Prime Minister Justin Trudeau threatened to cancel a multi-billion-dollar defence contract
President Erdogan's adviser dismissed the Saudi explanations as mockery
But several of Saudi Arabia's regional allies - including Kuwait and Egypt - have come out in its support.