He said the consulate was equipped with cameras but they did not record footage, so no images could be retrieved of Khashoggi entering or leaving the consulate, which is ringed by police barriers and has high security fences topped with barbed wire.
Saudi Arabia, which has denied the accusations, is under huge global pressure, including from the USA and the European Union, to support a "thorough and open" probe into the journalist's disappearance.
The 59-year-old Khashoggi went missing while on a visit to the consulate in Istanbul for paperwork to marry his Turkish fiancee.
Khashoggi has been missing since Tuesday when he had an appointment at the Saudi consulate to get papers needed to marry his Turkish fiancee.
Ryan's statement came hours after Turkey said it would search the consulate, an extraordinary probe of a diplomatic post that indicates the pressure Saudi Arabia faces over Khashoggi's disappearance. "I do not like it", Trump told reporters at the White House.
"[The] Saudi authorities said they were open to cooperation and that a search can be conducted at the consulate building", the ministry's spokesperson, Hami Aksoy, said in a statement, adding that the search will be conducted in "an intensive manner".
Turkey's President Tayyip Erdogan asked Saudi Arabia on Monday to prove its assertion that Khashoggi left the consulate.
Investigators reportedly believe that Mr Khashoggi's body might have been smuggled out of the consulate in diplomatic vans and then carried onto one of the planes. US Secretary of State Mike Pompeo said officials have taken up the matter with their Saudi counterparts. Khashoggi had relocated to the USA on October 2, 2017, fearing trouble (or even harm) from Saudi authorities - at the behest of Crown Prince Mohammed bin Salman (MBS) - for having remained a strong voice of dissent, always vociferous in castigating the Saudi government for its anti-people policies, severe Wahhabism, persecution of Houthis in Yemen, economic blockade of Qatar and myriad other problems.
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Turkey said it would search Saudi Arabia's consulate.
The Khashoggi family confirmed that they are coordinating with the Saudi government to learn about the latest developments in the case.
Many Turkish journalists and Qatari citizens criticized false stories being spread about the disappearance of Saudi journalist Jamal Khashoggi. "If he's in Saudi Arabia, I would know that".
Washington Post columnist David Ignatius recently noted that his friend Khashoggi had endured a crisis of conscience previous year when MBS was jailing and torturing his Saudi friends.
He said it comes as no surprise that Riyad is looking to quash criticism, but this case is beyond the sad but true usual jailing of journalists.
Saudi officials have denied that he was killed and earlier on Tuesday invited Turkish experts and related officials to visit the consulate, according to Turkey's state-owned news agency Anadolu. "Hopefully that will sort itself out". "Just met the Saudi ambassador to seek urgent answers over Jamal Khashoggi", foreign minister Jeremy Hunt said on Twitter.
The two countries have such an obligation under both criminal law and worldwide human rights law, she said. "I said nothing. I didn't want to lose my job or my freedom".
FILE - Saudi dissident Jamal Khashoggi speaks at an event hosted by Middle East Monitor in London, Sept. 29, 2018.
The alleged murder, cloaked in deep mystery, assumes more global significance because Khashoggi was a high-profile journalist with penetrating worldwide connections.