He said he believes Turkish officials soon will announce the findings of their investigation.
Government sources said police believe the journalist was killed inside the consulate.
Earlier on Tuesday, foreign secretary Jeremy Hunt met the Saudi ambassador, Prince Mohammed bin Nawaf Al Saud, to voice the UK's concern about the disappearance Mr Khashoggi. "I do not like it", Trump said.
Several news organizations have cited anonymous Turkish officials claiming that Khashoggi was the victim of a premeditated murder inside the consulate; Saudi officials have denied those allegations. The longer the crisis continues, the more biased Al-Jazeera gets, he said.
Mr Khashoggi, who was living in self-imposed exile in the U.S. and working for the Washington Post before his disappearance, was a frequent critic of the kingdom's de facto ruler Crown Prince Mohammed bin Salman, whom he described as a "brash and abrasive young innovator" who was "acting like Putin".
In recent days, Americans lawmakers from across the political spectrum have warned the affair could harm US-Saudi relations.
"As if the Saudi authorities were asleep and there was a unusual silence at a time when the news of Khashoggi's disappearance was spread in the world", he noted. He left Saudi Arabia a year ago after he said the authorities had instructed him to stop posting on Twitter.
It says the journalist left the consulate shortly after arriving, while Turkey says he was not seen leaving the building.
In the interview published Friday, October 5, the Saudi crown prince also said he understood that Khashoggi had entered the consulate "and he got out after a few minutes or one hour".
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Under MBS, Saudi Arabia has increasingly shown it will not tolerate any foreign criticism.
A member of the Saudi elite, he had remained in exile in the USA for much of the past year, from where he wrote columns for The Washington Post critiquing aspects of the Kingdom's reform programme.
The private DHA agency said the planes, which it identified as a two Gulfstreams belonging to a Riyadh-based company that hires private jets, landed at Istanbul's Ataturk Airport on the day Khashoggi vanished.
U.S. President Donald Trump said on Tuesday he plans to speak with the Saudis without elaborating.
President Donald Trump, who took his first overseas trip as USA president to the kingdom and whose son-in-law Jared Kushner has close ties to Prince Mohammed, said he had concerns.
Saudi Crown Prince Mohammed bin Salman said last week that Riyadh was "ready to welcome the Turkish government to go and search our premises", because it had "nothing to hide" about the missing journalist.
He added: "We trust the government and the actions taken, and all the efforts that are taken in the case of Jamal Khashoggi".
In a released audio snippet, he said he did not think he'd be able to ever return to his native country.
"Do you not have cameras and everything of the sort?"
The alleged murder, cloaked in deep mystery, assumes more global significance because Khashoggi was a high-profile journalist with penetrating worldwide connections. Saudi Arabia is ranked 169th out of 180 in the press freedom group Reporters Without Borders' latest World Press Freedom Index. "Jamal is a Saudi citizen whose safety and security is a top priority for the Kingdom".