Khashoggi, who lived in the United States as a legal permanent resident and worked for "The Washington Post", was last seen on October 2 entering his country's consulate in Istanbul. His fiancée was waiting outside for several hours.
Erdogan and Saudi King Salman spoke by phone on Friday night, agreeing to continue cooperation and exchanging details on the case, the Turkish presidency said in a statement.
How did they explain it?
The talk between Khashoggi and the suspect "did not go as required and escalated negatively which led to a fight between them and the citizen / Jamal Khashoggi, which aggregated the situation and led to his death".
Authorities say 18 Saudi suspects were in custody and intelligence officials had been fired.
Trump repeatedly touted the US$110 billion in weapons deals he announced during his visit to Saudi Arabia past year, and insisted around 500,000 U.S. jobs were at stake. He called for a USA investigation.
In a statement on Friday night, White House press secretary Sarah Huckabee Sanders said the United States will closely follow worldwide investigations into Mr Khashoggi's death and will advocate for justice that is "timely, transparent and in accordance with all due process".
But as the days dragged on and evidence of Khashoggi's death mounted, Trump's view began to shift, White House officials said.
Earlier this week, President Donald Trump cautioned against blaming Saudi Arabia for Khashoggi's disappearance but told reporters Thursday that "it certainly looks like" he was dead. People close to Khashoggi and the government said Qahtani had tried to lure the journalist back to Saudi Arabia after he moved to Washington a year ago fearing reprisals for his views.
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A USA government source said U.S. intelligence agencies are increasingly convinced of Prince Mohammed's culpability in the operation against Khashoggi, which they believe resulted in his death.
Were his remains to be found, traces of the drug may be found, asking new questions of Saudi Arabia's fist-fight narrative.
Graham has been one of the fiercest critics of Saudi Arabia on the Hill amid Khashoggi's disappearance and has warned he would pursue sanctions against the Kingdom while calling for Crown Prince Mohammed bin Salman - who reports allege is responsible for a plot to kill Khashoggi - to step down.
He has not been seen since visiting the Saudi consulate in Istanbul earlier this month to collect documents ahead of marrying his Turkish fiancee.
Turkish officials had said that the journalist - a Saudi citizen and USA resident - was killed and his body dismembered.
Saudi Arabia said it "expresses deep regret" over his death and King Salman put his son, Crown Prince Mohammed bin Salman, in charge of re-vamping the country's intelligence agency.
In Washington's first response to Saudi Arabia's confirmation that the US-based writer was dead, White House spokeswoman Sarah Sanders said merely that the U.S. "acknowledges the announcement".
The episode had threatened to create a diplomatic crisis with the US, which sees its alliance with Riyadh as the cornerstone of its Middle East policy, and Turkey, which has tenuous ties with Saudi Arabia. Khashoggi had gone to the consulate to get papers he needed to be married. "The Secretary-General is deeply troubled by the confirmation of the death of Jamal Khashoggi".