The murder of Mr Khashoggi, a Washington Post columnist and vocal critic of Saudi Arabia's de facto ruler Crown Prince Mohammed bin Salman, sparked worldwide outrage and threw the oil-rich nation into crisis.
Writing in The Washington Post on Friday, Cengiz said the United States should be leading the global community in seeking justice for Khashoggi.
After Saudi Arabia admitted that Khashoggi was killed in its Istanbul consulate, five high-ranking officials were dismissed, including bin Salman's media chief and the deputy head of the Saudi intelligence service.
The kingdom has faced a torrent of global condemnation over the murder of Khashoggi, upending the young Crown Prince Mohammed bin Salman's image as a reformer on the worldwide stage.
In a phone call about the case with both Jared Kushner, the president's son-in-law and Middle East adviser, and John Bolton, the national security adviser, Prince Mohammed argued that Khashoggi was a member of the Muslim Brotherhood, according to two people familiar with the call. Add Jamal Khashoggi as an interest to stay up to date on the latest Jamal Khashoggi news, video, and analysis from ABC News.
In Bulgaria on Friday, Israeli Prime Minister Benjamin Netanyahu called Khashoggi's slaying a horrendous act that "should be duly dealt with" in a way that doesn't undermine Saudi Arabia's stability. The Saudi government publicly has called his death a "terrible tragedy".
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Netanyahu has refrained from publicly weighing in on the murder by Saudi agents of journalist and regime critic Khashoggi at the Saudi consulate in Istanbul. But the White House intends to keep the sanctions limited enough to avoid a rupture in its partnership with Crown Prince Mohammed.
The journalist's family told the Post in response: "Jamal Khashoggi was not a member of the Muslim Brotherhood". A critic of the Saudi royal family, Khashoggi had been living in exile in the United States.
"The victim's body was dismembered and destroyed following his death by suffocation", the statement said.
Turkish officials appear to have dismissed a theory that Jamal Khashoggi's body was given to a mystery local collaborator in Istanbul.
The CHP leader was referring to the killing of Saudi journalist Jamal Khashoggi and the Saudi Consulate General to Istanbul, who left Turkey a few days after the disappearance of the journalist. Saudi public prosecutor Saud al-Mojeb offered a different explanation last week when he said the killing was premeditated. He entered the consulate to sort out documents for his marriage.
Ankara has repeatedly called for the suspects - who have been arrested in Saudi Arabia - to be extradited for trial in Turkey, something that Riyadh has rejected.