Fahrettin Altun, director of communications at the Turkish presidency, said on Monday Riyadh's refusal to extradite the suspects was very disappointing and would play into the hands of critics "who believe Saudi Arabia has been trying to cover up the murder".
Khashoggi, a critic of Saudi Arabia's de facto ruler Crown Prince Mohammed bin Salman, was brutally killed two months ago at the Saudi consulate in Istanbul when he went there to collect documents for his forthcoming marriage.
His body has not been found.
Altun told Reuters that Saudi authorities had not been sufficiently cooperative and Turkey has seen "little evidence of the Saudi prosecutors intending to shed light on what happened to Mr. Khashoggi".
Therefore "it will be in the best interest of the international community to seek justice for the late Saudi journalist under international law," Altun said.
Turkey's foreign minister said last month Ankara may seek a formal United Nations inquiry if its dealings with Saudi Arabia came to an impasse, but Altun's comments appeared to be the most direct call yet to widen the investigation.
Altun said Saudi intelligence operatives, including an autopsy expert, travelled to Istanbul for the specific purpose of killing Khashoggi. The Saudi consul "was apparently complicit in this crime", he added.
Turkish officials said last week that the Istanbul prosecutor's office had concluded there was "strong suspicion" that Saud al-Qahtani, a top aide to Prince Mohammed, and General Ahmed al-Asiri, who served as deputy head of foreign intelligence, were among the planners of Khashoggi's killing.
On Sunday, Saudi Arabia's Foreign Minister Adel al-Jubeir ruled out sending them to Turkey for trial. "We don't extradite our citizens," he said at a Gulf Arab summit in Riyadh.
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The international outrage over the poisoning of the Skripals in the UK has seen Russia take international sanctions on an unprecedented scale. We even had Simon Bridges barking on the radio that the Government had not been strong enough in our condemnation of that act. And now we have state actors having confessed to a murder and where are the sanctions? Where is Simon Bridges? Why is our media not baiting Jacinda Ardern into public proclamations of our country's standing this time around? Why is there always such blatant hypocrisy and bigotry in our society?