Turkish President Recep Tayyip Erdoğan and US President Donald Trump have agreed on the need to uncover all the circumstances of the killing of Saudi journalist Jamal Khashoggi in his consulate in Istanbul on October 2.

During a telephone conversation on Sunday evening, the two presidents stressed the need to disclose Khashoggi's case in all its aspects.

The Turkish presidency said Erdogan agreed with Trump that "all aspects" of the case of Saudi journalist Jamal Khashoggi should be clarified.

The conversation comes hours after the Turkish president vowed that he would announce next Tuesday all the facts about the killing of Saudi journalist Jamal Khashoggi, presenting the details "in a very different way."

"Why have 15 people come here (Istanbul) and why 18 people have been arrested (in Saudi Arabia)? All the details of these things should be disclosed," Erdogan said during a speech on Sunday at the opening of a project in Istanbul.

"I will talk about it very differently Tuesday during my speech before the parliamentary bloc (of the Justice and Development Party), and I will go into the details then."

"We will discuss all the details, and I will talk about everything that is being discussed about it in the international community, and about the parties that deal with it," he said.

Earlier on Sunday, a source in the Turkish prosecutor's office said the Turkish criminal investigation team had found evidence that fully supported the prosecutor's view of the murder of Jamal Khashoggi inside the Saudi consulate in Istanbul on October 2.

On Friday night, Saudi Arabia officially admitted Khashoggi's death inside the consulate, but said he died of "quarrels and handcuffing" and announced the arrest of 18 Saudis in custody.