Speaking to the Fox Business Network on Wednesday, Trump again cited counterterrorism cooperation with Saudi Arabia and the kingdom's contracts with US defense contractors.
While the president vowed to reporters that, "We are going to leave nothing uncovered" he suggested that "rogue killers" could've been behind Khashoggi's disappearance.
"The king firmly denied any knowledge of it", Trump told reporters Monday.
Turkish officials have said they believe he was killed - a claim Saudi Arabia has denied - with the controversy dealing a huge blow to the kingdom's image and efforts by its youthful crown prince to showcase a reform drive. Turkish officials have said he was killed and dismembered. Turkish officials reportedly said last week that they possess audio and video proof that The Washington Post columnist was interrogated, tortured and then murdered.
CNN saw a cleaning crew enter the main consulate building on Monday before Turkish officials arrived with a forensics team to begin their investigation.
Trump told the CBS news show 60 Minutes on Sunday that Saudi Arabia would face "severe punishment" if it is determined Khashoggi was killed inside the Saudi consulate, but Riyadh dismissed the USA threat and said it would retaliate if Trump took any action against Saudi Arabia.
Both men were seen smiling and exchanging pleasantries ahead of a closed-door meeting to discuss the case of Khashoggi, a Saudi citizen and USA resident. With such a lack of clarity, the administration has not ruled out any possible scenario. The official spoke on condition of anonymity because the investigation was ongoing.
"I am immediately sending our Secretary of State to meet with King!" Pompeo was due to arrive in the kingdom on Tuesday morning for his meeting with the king. While he's expressed concern about Khashoggi's disappearance, he said he refused to halt arms sales to the country.
Trump quoted the King on Monday as saying that neither he nor his son, Crown Prince Mohammed, had any information about what had happened to Khashoggi. He and Trump's son-in-law and senior adviser, Jared Kushner, have forged close ties.
Senate Majority Leader Mitch McConnell, R-Ky., also predicted USA backlash if a Saudi link is proved, but he said Congress is awaiting details from Pompeo on his meetings. A Saudi-owned satellite channel later suggested the world's largest oil exporter could wield that production as a weapon against America.
He was last seen on surveillance footage entering the main entrance of the Saudi Consulate in Istanbul.
CNN reported that the Saudis were going to admit the killing had occurred but deny the king or crown prince had ordered it, which does not match what analysts and experts know about the kingdom's inner workings.
The New York Times said Prince Mohammed had approved an interrogation or abduction of Khashoggi and the government would shield him by blaming an intelligence official.
Khashoggi has written extensively for the Post about Saudi Arabia, criticizing its war in Yemen, its recent diplomatic spat with Canada and its arrest of women's rights activists after the lifting of a driving ban for women. "Answers will be forthcoming shortly", Trump said in a tweet. "I've heard that report but nobody's knows if it's an official report".
Turkey has wanted to search the consulate for days.
"We encourage Turkish-Saudi collaboration and look forward to the Kingdom of Saudi Arabia conducting a thorough, credible, transparent, and prompt investigation, as announced".
Mohammed al-Otaibi, the Saudi consul general, apparently left on a 2pm flight as security forces set up barricades outside his residence in the city.
Turkish President Tayyip Erdogan raised the possibility that parts of the consulate had been repainted since Khashoggi disappeared.
Prince Mohammed has aggressively pitched the kingdom as a destination for foreign investment. But Khashoggi's disappearance has led several business leaders and media outlets to back out of an upcoming investment conference in Riyadh.
In a major new blow for the event, JPMorgan Chase CEO Jamie Dimon and Ford chairman Bill Ford also cancelled plans to attend as well as Larry Fink, the head of investment giant BlackRock, and Steve Schwarzman of Blackstone.