"We also demand Saudi Arabian government to release journalists and activists in detention and stop the repression of dissent".
The killing of Khashoggi, a Washington Post columnist and a critic of Saudi Arabia's de facto ruler, Crown Prince Mohammed bin Salman, has sparked global condemnation and mushroomed into a major crisis for the world's top oil exporter.
Khashoggi, a Saudi journalist who was often critical of Riyadh in his reporting, was killed in the Saudi Consulate in Istanbul earlier this month.
"The Prime Minister also reiterated that all individuals bearing responsibility for the killing of Mr Khashoggi must be properly held to account..."
Erdogan announced that Khashoggi's "ferocious murder" had been "planned", rejecting the Saudi explanation of his death occurring due to a brawl within the consular premises. Khashoggi, who lived in self-imposed exile in the United States for almost a year before his death, had written critically of Prince Mohammed's crackdown on dissent.
"I am not satisfied with what I've heard", Trump said.
While Turkish officials, speaking anonymously, and some senior USA lawmakers have suggested the crown prince himself likely had a role in approving the killing, a confident sounding Prince Salman vowed on Wednesday that the kingdom run by his family for nearly 100 years would help get to the bottom of what he called a "heinous crime".
First, Saudi officials said Khashoggi left the embassy unharmed, but after 17 days, following grisly news reports of Khashoggi's death, Saudi officials said last Friday that he was killed during an altercation inside the consulate.
Saudi officials on Wednesday allowed Turkish police to examine a well in the garden of the kingdom's consulate in Istanbul, after initially refusing to give permission to the investigators.
Turkish President Recep Tayyip Erdogan on Tuesday laid out his country's initial findings in its investigation, saying Khashoggi's murder was "premeditated".
The case has cast scrutiny on Saudi Crown Prince Mohammed bin Salman after Middle East Eye revealed that at least seven of the 15 suspects who flew to Istanbul were members of his personal security detail.
Asked by a reporter in the White House Oval Office how the Khashoggi killing could have happened, Trump said: "They had a very bad original concept".
Mr Erdogan stopped short of mentioning the crown prince who some USA lawmakers suspect ordered the killing. His dismembered body parts have been recovered from the Saudi consul general home, a UK-based broadcaster said.
"The Saudi administration has taken an important step by admitting to the murder".