The overnight announcements in Saudi state media came more than two weeks after Khashoggi entered the Saudi consulate in Istanbul for paperwork required to marry his Turkish fiancée, and never came out.
Much of the reporting to date has relied on anonymous officials, often Turkish ones, and Turkish state-run media.
Prosecutors say 18 Saudis are being held as suspects in columnist Jamal Khashoggi's death, Royal court adviser Saud al-Qahtani and deputy intelligence chief Ahmed Asiri have been fired; Benjamin Hall reports from Istanbul.
Saudi King Salman ordered the formation of a ministerial committee, which Crown Prince Mohammed will head, to restructure the general intelligence agency, according to SPA.
"It offers no consolation to have Saudi officials confirm what the whole world already knows-Jamal Khashoggi was murdered inside the Saudi consulate in Istanbul".
Earlier this week, the Turkish pro-government newspaper Yeni Safak, citing what it described as an audio recording of Khashoggi's slaying, said a Saudi assassination squad seized the journalist after he entered the consulate, cutting off his fingers and later decapitating him.
The disappearance of Khashoggi has provoked global criticism of Saudi Arabia's de-facto ruler, Crown Prince Mohammed bin Salman, and convulsed the kingdom as it struggles to respond to increasing worldwide pressure to explain the journalist's fate.
In a flurry of coordinated statements, issued in the dead of night in Riyadh, Saudi Arabia claimed Khashoggi's death was accidental.
An undisclosed number consulate employees in Istanbul were interviewed by prosecutors, the semiofficial Anadolu news agency reported, a day after Turkish authorities began combing through wooded areas outside Istanbul in an apparent search for Khashoggi's remains.
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The kingdom announced that 18 people had been arrested in the ongoing investigation.
Calling Saudi Arabia a crucial ally against Iran that purchases billions of dollars-worth of United States weapons, Donald Trump lamented Khashoggi's "unacceptable" death but praised Riyadh for making the first arrests in the ongoing probe.
A Conservative MP in the county is facing questions over payments of more than £40,000 he received as an advisor to an organisation based in Saudi Arabia.
Trump sent Secretary of State Mike Pompeo earlier in the week to Riyadh, where the top U.S. diplomat praised the Saudis for conducting a probe and called for the two nations to maintain a close alliance for the sake of business deals and their shared opposition to Iran.
Eighteen Saudi citizens have also been detained in connection with the death.
Mr Trump says he finds the Saudi statement credible and will be speaking to the crown prince.
"The Secretary-General stresses the need for a prompt thorough and transparent investigation into the circumstances of Mr Khashoggi's death and full accountability for those responsible".
It's unclear whether the Saudi announcement will be enough to staunch the criticism the kingdom faces from lawmakers in the United States, its most crucial ally. "But I would prefer that we don't use as retribution, canceling the $110 billion-worth of work, which means 600,000 jobs".
Kushner does have close ties to the Saudis and its crown prince, Mohammed bin Salman, but there has been no evidence that he has any involvement with the suspected murder of Khashoggi. Arab allies have rallied to Riyadh's support, but Western pressure has intensified on Saudi Arabia to provide convincing answers.