Prince Mohammed said in an interview with Bloomberg published Friday that the journalist had left the consulate and Turkish authorities could search the building, which is Saudi sovereign territory.
A senior Turkish police source told MEE that Khashoggi had been "brutally tortured, killed and cut into pieces. We believe that the murder was premeditated and the body was subsequently moved out of the consulate".
Saudi Arabia's consul-general previously said his country was helping to search for Mr Khashoggi and dismissed talk of abduction.
Khashoggi disappeared after entering the diplomatic mission on Tuesday.
He claimed that Khashoggi had left the building not long after he entered earlier this week, alleging, "If he's in Saudi Arabia, I would know that".
Turkish police investigating the case had said in a statement yesterday that 15 Saudis, including several officials, arrived in Istanbul on two planes and visited the consulate while Khashoggi was inside.
The journalist said he had been banned from writing in the pan-Arab Al-Hayat newspaper, owned by Saudi prince Khaled bin Sultan al-Saud, over his defence of the Muslim Brotherhood which Riyadh has blacklisted as a terrorist organisation.
Khashoggi, a 59-year-old veteran journalist who has lived in self-imposed exile in the USA since Prince Mohammed's rise to power, disappeared October 2 while on a visit to the consulate to get paperwork done to be married to his Turkish fiancée.
On Saturday, Yasin Aktay, Erdogan's AK Party adviser and a friend of Khashoggi, told Qatari broadcaster Al Jazeera: "We demand a convincing clarification from Saudi Arabia, and what the crown prince offered is not convincing".
The Committee to Protect Journalists said it was alarmed by reports Khashoggi may have been killed inside the consulate.
He also stressed that with the support of Washington, Saudi Arabia was totally safe, but without USA, who knew what's going to happen. In an interview with Bloomberg, an American news service, MBS underscored that Riyadh "will pay nothing" to Washington for Saudi Arabia's security. Turkey has supported Qatar amid a yearlong boycott by Bahrain, Egypt, Saudi Arabia and the United Arab Emirates over a political dispute. It's there since 1744; I believe more than 30 years before the United States of America, And I believe, and I' m sorry if anyone misunderstands that, but I believe President (Barack) Obama, in his eight years, he worked against many of our agenda not (only) in Saudi Arabia, but also in the Middle East. "Until otherwise demonstrated, he is still inside the Saudi consulate in Istanbul and the Saudi authorities are responsible for his safety and well-being", she said in a statement.
Human rights groups have urged Riyadh to shed light on Khashoggi's whereabouts.
Khashoggi maintained ties with Saudi elites, including those in its intelligence apparatus, and launched a satellite news channel, Al-Arab, from Bahrain in 2015 with the backing of Saudi billionaire Prince Alwaleed bin Talal.