A year after Khashoggi was killed inside the Saudi consulate in Istanbul, Erdogan said the murder "was arguably the most influential and controversial incident of the 21st century".
"That, one year on, the international community still knows very little about what happened is a serious source of concern. Whether all aspects of the Saudi journalist's death will ever come to light will determine what kind of world our children live in," Erdogan wrote in an opinion article published by the Washington Post on Sunday.
The Turkish president suggested the killing was carried out by agents of a "shadow state" in Saudi Arabia.
"My administration ... made a clear and unmistakable distinction between the thugs who murdered Khashoggi and King Salman and his loyal subjects," he said.
Erdogan said Turkey continued to see Saudi Arabia as a friend and ally, but that it did not mean Ankara would remain silent.
Pledging to continue efforts to shed light on the case, Erdogan repeated his questions from a similar article published last year: "Where are Khashoggi's remains? Who signed the Saudi journalist's death warrant? Who dispatched the 15 killers, including a forensic expert, aboard the two planes to Istanbul?"
He said it was "in the best interest of humanity" to ensure such crimes are not committed again.
"Combating impunity is the easiest way to accomplish that goal. We owe it to Jamal's family," Erdogan wrote.
Al Jazeera's Sinem Koseoglu, reporting from Istanbul, said a change of tone was noticeable in Erdogan's remarks.
"Last year, after this brutal murder, Turkey had harsh statements against Saudi Arabia. In this article, President Erdogan made it clear he never thought King Salman ordered the killing. And he never mentioned the crown prince, Mohammed bin Salman [MBS], which is interesting," she said.
Eleven Saudi suspects have been put on trial in secretive proceedings but only a few hearings have been held. A report by the United Nations has called for MBS and other senior Saudi officials to be investigated.
The CIA and some Western governments have said they believe Prince Mohammed ordered the operation, an assertion Saudi officials have repeatedly denied.
In an interview with United States broadcaster CBS, the crown prince said he had "absolutely not" ordered the killing, although he bore responsibility as leader of his country.
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