Members of Congress have demanded that sanctions be imposed on Saudi Arabia over the killing of Khashoggi, who lived in self-imposed exile in the USA and wrote critically about Saudi Crown Prince Mohammed bin Salman.
US President Donald Trump said the Saudis had a "very bad original concept" in killing the 59-year-old Saudi insider-turned-critic.
"Those behind this crime will be held accountable ... in the end justice will prevail".
Mr Trump said he wanted to believe Prince Mohammed when he said that lower level officials were to blame for the killing at the Saudi mission.
The state-run Saudi Press Agency said: 'Discussions took place with the citizen Jamal Khashoggi during his presence in the consulate of the kingdom in Istanbul by the suspects (that) did not go as required and developed in a negative way, leading to a fist fight.
Saudi state media on Tuesday published photos of Jamal Khashoggi's son Salah Khashoggi with Saudi Arabia's King Salman and Prince Mohammed.
Addressing a panel at the Future Investment Initiative conference in Riyadh, Prince Mohammed said that many parties were trying to exploit the incident to "drive a wedge between Saudi Arabia and Turkey".
Turkey's President Recep Tayyip Erdogan insisted on Wednesday his country would not allow those responsible for Jamal Khashoggi's killing to avoid justice, keeping up pressure on Riyadh amid global skepticism over varying Saudi accounts of the prominent journalist's death.
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Eighteen days after Khashoggi disappeared, Saudi Arabia acknowledged that the writer is dead.
Prince Mohammed said Wednesday that the killing of Khashoggi is a "heinous crime that can not be justified".
This narrative has been met with a great deal of skepticism and was directly contradicted by Turkish President RecepTayyip Erdogan on Tuesday when he said Khashoggi's killing was premeditated.
"We know that many are trying to use this painful thing to create a kind of wedge between Saudi Arabia and Turkey", he said.
The Saudi government has blamed the murder on rogue agents, but the Turkish president said this was a "political murder" by Saudi intelligence officers and officials.
Secretary of State Mike Pompeo said at a news conference Tuesday the US has identified people implicated in the killing - "including those in the intelligence services, the royal court, the foreign ministry and other Saudi ministries" - and is working to hold them accountable. He did not refer to an audio recording in his speech in parliament.