Turkish officials say they fear Khashoggi was killed and dismembered inside the Istanbul consulate.
Saudi authorities have yet to give a clear explanation of Khashoggi's fate, while several countries - particularly Turkey, the USA, and the U.K - are pressing the case to be cleared up as soon as possible.
Khashoggi also advised Prince Turki al-Faisal al-Saud, the former longtime head of Saudi intelligence who served as Saudi ambassador to Britain and then the United States in the 2000s.
The family of missing Saudi journalist Jamal Khashoggi on Tuesday called for an global investigation into the circumstances of his disappearance.
The search came after Turkish President Recep Tayyip Erdogan and King Salman also had their first telephone talks since the controversy erupted, in what appeared to be a conciliatory conversation, according to official readouts.
And it could help Turkey, where a shaky economy would benefit from a financial infusion that low-interest loans from Riyadh could provide.
Jamal Khashoggi, a prominent critic of Saudi Crown Prince Mohammad bin Salman and a USA resident, disappeared on October 2 after visiting the Saudi consulate in Istanbul. The Saudis, for two weeks, denied that he vanished inside their consulate, calling accusations that he was killed there, "lies and baseless allegations". Christopher Murphy, D-Conn., wrote in a Twitter post.
Trump spoke with King Salman of Saudi Arabia on Monday morning in a 20-minute phone call.
"It sounded to me like maybe these could have been rogue killers - who knows", Trump said, speaking to reporters as he headed to visit areas in Georgia and Florida that were ravaged by Hurricane Michael. President Trump publicly called for the Saudis to choose NY for the listing of 5 percent of Saudi Aramco and bragged repeatedly about the $110 billion arms deal he claims to have brokered during his visit to Riyadh, the Saudi capital, in 2017. "Who knows? We're going to try getting to the bottom of it very soon".
Until now, Riyadh has not allowed Turkish investigators to search the consulate - officially Saudi territory - with reports both sides were at odds over the conditions.
Turkish police investigators entered the Istanbul consulate late on Monday.
But US media reported on Monday that the kingdom is considering an admission that Khashoggi died after an interrogation that went wrong during an intended abduction.More news: Tom Thibodeau Goes Off on Media Regarding Jimmy Butler Rumors
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"All I can do is report what he told me", Trump told reporters on Monday, adding that he warned the Saudi king that "the world is watching".
Trump dispatched Secretary of State Mike Pompeo to meet King Salman over the case that has strained the Americans' relationship with the Saudis, carefully cultivated by the U.S. president.
"Determining what happened to Jamal Khashoggi is something of great importance to the president", State Department spokeswoman Heather Nauert said on Monday as Pompeo prepared to depart Washington. The Saudis are the biggest buyers of US military hardware in the world.
The Saudi Embassy in Washington also canceled its National Day party, which was scheduled for Thursday.
Relations between Canada and Saudi Arabia have been tense in recent months. Their actions followed a similar move by the Harbour Group last week. Khashoggi worked closely on media initiatives with Prince Alwaleed bin Talal, the billionaire businessman detained in the November roundup of dozens of influential business executives and ruling-family members by MBS.
He had been critical of Prince Mohammed, who has cracked down on dissent with arrests.
"Many in Washington have reached the conclusion that this is a guy we can't do business with", said Gerald Feierstein, the director for government relations, policy and programs at the Middle East Institute, a nonpartisan think tank, and a former USA ambassador to Yemen.
Turkish authorities have an audio recording indicating that Khashoggi was killed in the consulate, a Turkish official and a security source told Reuters, and have shared evidence with countries including Saudi Arabia and the United States.
Saudi Arabia has denied any involvement in Khashoggi's disappearance and claimed that he left the consulate, though it provided no evidence. The U.S. news network cited two unnamed sources.
Khashoggi's fate has troubled Washington and Saudi Arabia's other traditional Western allies.
For the Trump administration, Khashoggi's case risks top foreign-policy priorities. "Think of that, $110 billion". And ensuring Riyadh's willingness to increase oil production so that coming sanctions on Iranian oil do not lead to a surge in gas prices has been at least as important.
US Treasury Secretary Steven Mnuchin said he still plans to attend but would "take (it)... into account" if more information came out. Some U.S. companies that had planned to attend the conference, including The New York Times, have pulled out since Khashoggi's disappearance. The columnist is one of the best-known news-media personalities in the kingdom and has been a confidant to several previous kings and princes.