Reports emerged about a Saudi hit squad killing and dismembering the journalist - allegedly on the orders of the crown prince.
He called the killing "a heinous crime" that was "really painful to all Saudis" and to "every human being in the world".
"It is a heinous crime that can not be justified".
He declined to say whether the crown prince, sometimes known by his initials MBS, would be among those penalized, despite comments from many members of Congress that he must have known about or even ordered the plot.
A Saudi cabinet meeting chaired by King Salman said Riyadh would hold to account those responsible for the killing and those who failed in their duties, whoever they were. His other son, Sahel Khashoggi, was also in attendance.
Turkish President Tayipp Erdogan is shedding light on his government's probe into the death of journalist Jamal Khashoggi. But Secretary of State Mike Pompeo said the United States has identified some of the Saudi government and security officials it believes were involved in Mr Khashoggi's murder and would take appropriate actions including revoking U.S. visas.
"We are determined not to allow any cover up of this murder and for all those responsible from those who gave the command to those who executed it - not to escape justice", he said.
Dozens of Western politicians, top world bankers and company executives boycotted this year's Future Investment Initiative conference that opened in Riyadh on Tuesday, but the world's largest oil exporter showed it could still do business by signing deals worth US$50 billion (S$68.96 billion) on the first day.
Many global business leaders have pulled out of attending the summit over Khashoggi's slaying.
Saudi Arabia has admitted he was killed there, but Khashoggi's body has not yet been found.
The Turkish President stated that a team of three Saudis arrived in Istanbul on a chartered flight and settled into a hotel on October 1, a day before Khashoggi went missing from the Saudi consulate in Turkey.
On Monday, Saudi Arabian officials said they do not know details of how dissident journalist Jamal Khashoggi was killed in their consulate in Istanbul or where his body was.
Attiah added that Khashoggi had told her that what "saddened him the most was the fact Saudi Arabia imposed travel bans on his kids after he started writing for" The Post. The investment forum is aimed at attracting investors to help underwrite that effort. The crown prince, already a controversial leader in relation to his crackdowns on dissent and the Saudi role in the war in Yemen, is suspected of orchestrating Khashoggi's killing.
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