Saudi Arabia's chief prosecutor, Erdogan said, will arrive Sunday in Istanbul as part of the investigation.
Meanwhile, Turkey on Friday intensified its demands for Saudi Arabia to extradite 18 suspects in the killing of journalist Jamal Khashoggi, a call that is likely to be met with resistance from the kingdom and could escalate tensions between the US-allied regional powers.
Khashoggi was last seen entering the Saudi consulate in Istanbul on October 3 to get documents for his marriage, and Turkish sources have claimed that he was killed.
The president also said it was "possible" Crown Prince Mohammed bin Salman did not know about the killing.
The Saudi state is responsible for the murder of journalist Jamal Khashoggi and can not "wash its hands" of responsibility, UN Special Rapporteur on Extrajudicial, Summary or Arbitrary Execution Agnes Callamard said at the UN headquarters in New York City on Thursday.
US and foreign officials say such an operation - involving a team of Saudi agents - was unlikely to have taken place without the knowledge of the kingdom's leaders, including ambitious Crown Prince Mohammed bin Salman.
"Failure of any nation to adhere to global norms and the rule of law undermines regional stability at a time when it is needed most", he stressed.
"We will prove to the world that the two governments (Saudi and Turkish) are cooperating to punish any criminal, any culprit, and at the end justice will prevail", he said to applause.
Erdoğan said Friday that Turkey would reveal more evidence about the killing but was not in any rush to do so, indicating that Turkish authorities will methodically increase pressure on Saudi Arabia even as the kingdom floats conflicting statements in a vain and often clumsy attempt to end the crisis.
The statement from Saudi prosecutors that evidence showed Khashoggi's killing was premeditated contradicted an earlier Saudi assertion that rogue officials from the kingdom had killed Khashoggi by mistake in a brawl.
"Yes Trump invited me to the United States during the first days of the investigation" she said.
A string of gruesome details about the murder have continued to appear in the Turkish media.
"Unfortunately, there has been this hysteria in the media about Saudi Arabia's guilt before the investigation is completed", he said.
He also said Riyadh needs to disclose the identity of its "local cooperator" who purportedly took Khashoggi's body from Saudi agents after the journalist was killed at the consulate in Istanbul on October 2.
She also said she had declined an invitation to meet Donald Trump, saying the US President was not honest about investigating the killing. The kingdom's leadership has pushed responsibility down the chain of command. "Our secretary of state has already revoked visas and will be taking additional measures".
Now, Turkish broadcast CNN Turk said police in Istanbul were investigating water samples from the 12m well after initially being denied access.