The public prosecutor said 18 people, all Saudi nationals, have been detained in connection to the probe.
In his final column for The Washington Post, which was published weeks after his disappearance, Khashoggi wrote: "The Arab world is facing its own version of an Iron Curtain, imposed not by external actors but through domestic forces vying for power". He was last seen entering the Saudi consulate in Istanbul, Turkey, where he went to receive papers he needed to remarry. "We expect the Saudi government to cooperate fully with Turkish authorities regarding the investigation of this matter".
Al-Asiri was a senior adviser to Crown Prince Mohammed bin Salman, as was another official fired over the incident, Saud al-Qahtani, who was in charge of Saudi propaganda overseas.
The announcement could ease strains with the US and Turkey but leaves lingering questions about the extent of Prince Mohammed's role in and knowledge of the incident.
Maas has also called into question the sale of arms to Saudi Arabia.
Saudi Arabia has plunged into an worldwide crisis over the fate of Khashoggi, who was critical of the crown prince. It comes despite the claims of Turkish officials who have said they have evidence of his killing, including an audio recording of Khashoggi's death.
Khashoggi went into self-imposed exile in June 2017 just as bin Salman was elevated to Crown Prince.
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Britain's Foreign Office, which also has close ties to Riyadh, said it "was a bad act and those responsible must be held to account".
"We're seeing a lot of countries taking now a much more dim view of their business relationship with Saudi Arabia", MacKay said. When asked if sanctions on Saudi Arabia are possible, Trump said they "could be, could be".
Trump's comments about the Khashoggi incident in recent days have ranged from threatening Saudi Arabia with "very severe" consequences and warning of economic sanctions, to more conciliatory remarks in which he has played up the country's role as a U.S. ally against Iran and Islamist militants, as well as a major purchaser of United States arms.
Turkish authorities also denied Friday they have shared with US officials an audio recording of the torture and killing of Khashoggi.
Democratic Representative Adam Schiff of California said Saudi Arabia's claim that Mr Khashoggi died in a brawl was not credible. It also contradicted leaked information from unnamed Turkish security sources that Khashoggi was tortured, killed and dismembered inside the building.
US President Donald Trump indicated he believed the Saudi narrative was credible.
"We will continue to closely follow the worldwide investigations into this tragic incident and advocate for justice that is timely, transparent and in accordance with all due process", she said. "And once we've identified the fact set, then they have the responsibility and the first instance to hold accountable those inside the country that may have been involved in any wrongdoing".
Observers said the strategy Turkey deployed over Khashoggi's killing - controlled leaks to the media - gives it political leverage over Saudi Arabia - Ankara and Riyadh are at odds on a number of regional issues, including a Saudi-led boycott of Qatar and relations with Iran.
The Times report takes a broad look at alleged Saudi government efforts to silence dissidents on Twitter.