Riyadh provided no evidence to support its account of the circumstances that led to Khashoggi's death and it was still unclear whether other governments would be satisfied with it.
Turkish officials suspect Khashoggi, a critic of the powerful Crown Prince Mohammed bin Salman, was tortured and killed inside the consulate by Saudi agents. His body has yet to be found.
Some Western governments and politicians gave guarded or skeptical responses to the Saudi explanation, but Middle Eastern allies closed ranks around the kingdom.
US President Donald Trump, who has forged close ties with the world's top oil exporter and made Prince Mohammed a centerpiece of his foreign policy, said the Saudi account was credible.
"I think it's a good first step, it's a big step," Trump said in Arizona. "Saudi Arabia has been a great ally. What happened is unacceptable."
Trump said he would speak with the crown prince, the kingdom's de facto ruler. But Trump again emphasized Riyadh's role in countering regional rival Iran and the importance a lucrative US arms sales to Saudi Arabia for American jobs.
Khashoggi, a US resident and Washington Post columnist, went missing after entering the consulate on Oct. 2 to obtain documents for his upcoming marriage.
Days later, Turkish officials said they believed he was killed in the building and his body cut up, an allegation Saudi Arabia had, until now, strenuously denied.
The Saudi public prosecutor said on Saturday that a fight broke out between Khashoggi and people who met him in the consulate, leading to his death. Eighteen Saudi nationals had been arrested, the prosecutor said in a statement.
A Saudi official told Reuters separately: "A group of Saudis had a physical altercation and Jamal died as a result of the chokehold. They were trying to keep him quiet."
Turkish investigators, who have been combing a forest and other sites outside Istanbul, are likely to find out what happened to Khashoggi's body "before long," a senior Turkish official told Reuters on Saturday.
The state of the body when found, could make it difficult to ascertain whether the Saudi account of the killing is accurate if it has indeed been dismembered.
Saudi state media said King Salman had ordered the dismissal of five officials, including Saud al-Qahtani, a royal court adviser seen as the right-hand man to Crown Prince Mohammed, and deputy intelligence chief Ahmed Asiri.
Some US lawmakers were unpersuaded by the Saudi account.
"To say that I am skeptical of the new Saudi narrative about Mr. Khashoggi is an understatement," Republican US Senator Lindsey Graham said.
Democrat Senator Jack Reed, said the Saudis were still not forthcoming with the truth. "This appears to have been a deliberate, planned act followed by a cover-up," he said.
AUDIO RECORDING
Turkish sources say the authorities have an audio recording purportedly documenting Khashoggi's murder inside the consulate. Pro-government newspaper Yeni Safak, citing the audio, said his torturers cut off his fingers during an interrogation and later beheaded him.
The crisis prompted the king to intervene, five sources with links to the Saudi royal family told Reuters.
The king also ordered a restructuring of the intelligence, to be led by Prince Mohammed, suggesting the prince still retained wide-ranging authority.
Before the Saudi announcements, Trump had said he might consider sanctions although he has also appeared unwilling to distance himself too much from the Saudi leadership. The White House said it would continue to press for "justice that is timely, transparent, and in accordance with all due process." For other Western allies, a main question will be whether they believe Prince Mohammed, who has painted himself as a reformer, has any culpability. King Salman had handed the day-to-day running of Saudi Arabia to his son.
Britian said it was considering its "next steps," while Australia said it pulled out of a planned investment summit in Saudi Arabia in protest at the killing.
Amnesty International said the Saudi explanation appeared to be a whitewash of "an appalling assassination."
The Saudi findings "marks an abysmal new low to Saudi Arabia's human rights record," its Middle East director said.
Regional allies - including Egypt, Bahrain and the United Arab Emirates - issued statements in praise of the king.
'NO ORDERS TO KILL HIM'
The dismissed official Qahtani, 40, rose to prominence after latching onto Prince Mohammed, becoming a rare confidante in his inner circle.
Sources say Qahtani would regularly speak on behalf of the crown prince and has given direct orders to senior officials including in the security apparatus.
People close to Khashoggi and the government said Qahtani had tried to lure the journalist back to Saudi Arabia after he moved to Washington a year ago fearing reprisals for his views.
Qahtani wrote on Twitter in August 2017: "Do you think I make decisions without guidance? I am an employee and a faithful executor of the orders of my lord the king and my lord the faithful crown prince."
In a tweet on Saturday, he thanked the king and crown prince for the "big confidence" they had in him.
Asiri joined the Saudi military in 2002, according to Saudi media reports, serving as spokesman for a coalition backing Yemen's ousted president after Prince Mohammed led Saudi Arabia into that country's civil war in 2015. He was named deputy chief of foreign intelligence in April 2017.
The prince had no knowledge of the specific operation that resulted in Khashoggi's death, a Saudi official familiar with the Saudi investigation said.
"There were no orders for them to kill him or even specifically kidnap him," said the official, speaking on condition of anonymity. There was a standing order to bring critics of the kingdom back to the country, he added.
"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 official said the whereabouts of Khashoggi's body were unclear after it was handed over to a local operator but there was no sign of it at the consulate.
"We don’t know for certain what happened to the body."
In Saudi Arabia, there was widespread support for the king and the crown prince on Twitter, with hashtags such as "#I am Saudi and I defend it" and "#Saudi kingdom of justice" trending.
For her part, Khashoggi's Turkish fiancée, Hatice Cengiz, tweeted in Arabic: "The heart grieves, the eye tears, and with your separation we are saddened, my dear Jamal," she said, also asking "#where is martyr Khashoggi's body?"