The Turkish president, Recep Tayyip Erdoğan, has made fresh demands on Saudi Arabia to disclose the location of Jamal Khashoggi’s body and identify who ordered his killing, in a sign that Ankara is willing to keep up the pressure on the beleaguered kingdom.

Eighteen men arrested in Saudi Arabia “must know” who killed the journalist and where his remains were taken, Erdoğan said in parliament on Friday, adding that the person who “gave the orders” for the alleged murder must be brought to justice and the suspects extradited for trial in Istanbul.

Riyadh’s changing accounts of what happened have been “comic”, the president said, calling them “childish statements … not compatible with the seriousness of a nation state”.

“Who gave that order? If you want to eliminate the suspicion [about you], the key question is these 18 people,” Erdoğan said. “You know how to make people talk,” he added, in a reference to the powerful Saudi crown prince, Mohammed bin Salman.

“But if you cannot make them talk, then hand them over to us. This incident happened in Istanbul. Let us put them on trial.”

Erdoğan also urged the Saudis to identify the “local collaborator” whom they say disposed of Khashoggi’s remains.

His pointed remarks come after he spoke to the heir to the Saudi throne for the first time on Wednesday about cooperating in the evolving diplomatic crisis.

Erdoğan has used the case to exert pressure on his Saudi rival, whom many believe must at a minimum have been aware of the operation, which involved several members of his personal guard and other senior officials.

Jamal Khashoggi disappeared inside the Saudi consulate this month. Photograph: Hasan Jamali/AP

Riyadh has gone to great lengths to insulate Prince Mohammed from any responsibility for Khashoggi’s death.

After various denials and explanations for what happened to the dissident Saudi writer when he attended a consulate appointment in Istanbul this month, Saudi Arabia said for the first time on Thursday the investigation’s evidence pointed to a “premeditated” killing.

Riyadh had previously said Khashoggi died during a fight with Saudi officials carrying out a rogue extradition operation, and that his body was rolled up in a rug and disposed of by an unidentified third party.

Turkish investigators allege Khashoggi was tortured before his death and his body dismembered with a bone saw by a 15-man hit team.

Saudi Arabia’s shifting story has been met with scepticism by Ankara and much of the rest of the international community. Earlier this week Erdoğan said Turkish investigators had clear evidence Khashoggi was murdered in a premeditated, political crime.

The Saudi admission on Thursday raised further questions as to who in the Saudi establishment had the authority to order an international murder operation.

Police have focused the search for the journalist’s remains on a well in the garden of the nearby consul general’s residence and woodland areas outside the city, but without any breakthroughs so far.

There are several avenues of investigation that have yet to be explored, Erdoğan told members of his AK party in Friday’s address.

Riyadh is sending the Saudi public prosecutor to Istanbul on Sunday to assist the investigation.

On Thursday it emerged Khashoggi’s eldest son had left Saudi Arabia for the US. Salah Khashoggi, who holds dual Saudi-US citizenship, had been barred from travelling outside the kingdom in recent months. Earlier in the week he was summoned to receive condolences from the crown prince.