Secretary of State Mike Pompeo also had a follow-up call with the Saudi's de facto leader.
"And we want do get to the bottom of it", the United States president said.
The case surrounding the missing Washington Post columnist who disappeared after entering a Saudi consulate in Istanbul, Turkey, raised more concerns in the USA after mounting evidence suggested he was murdered during the visit.
Earlier on Wednesday, Turkish media outlets published CCTV footage which they say shows evidence of a plot linked to Mr Khashoggi's disappearance. Trump said that Khashoggi's fiancée had sent him a letter and may come to the White House soon. "We will continue to monitor this situation and provide updates as available", she said.
USA intelligence intercepted communications between Saudi officials discussing a plan to capture journalist Jamal Khashoggi prior to his disappearance last week in Turkey in a case now roiling global investigators and threatening to damage relations between Washington and Riyadh.
Harsh actions against one of Trump's stalwart allies would be a sharp contrast with the administration's relatively muted tone over the kingdom's role in the war in Yemen and a crackdown on internal dissent.
Groups of men thought to be Saudi are seen entering Turkey via Istanbul airport, checking in at hotels and later leaving the country. The channel said the van then drove some 2 kilometers (1.2 miles) to the consul's home, where it parked inside a garage.
While Riyadh claimed he had left the consulate after his visit, Turkish police said Khashoggi did not emerge from the building. Trump visited Saudi Arabia in May 2017, and Mohammad has applauded his decision to withdraw from the Obama Administration's nuclear arms agreement with Iran.
A pro-government Turkish daily on Wednesday published preliminary evidence from investigators it said identified a 15-member Saudi intelligence team involved in the unexplained disappearance of journalist Jamal Khashoggi.
A Saudi Arabian flag flies over the Saudi Arabian consulate in Istanbul on October 10.
Aksam newspaper also published blurred photos of a jet arriving in Istanbul before dawn on October 2, carrying what it said were nine members of the Saudi team, as well as images of some of them checking in at a hotel.
"At this time, I implore President Trump and first lady Melania Trump to help shed light on Jamal's disappearance".
In a column published Wednesday by the Post, Hatice Cengiz wrote: "I also urge Saudi Arabia, especially King Salman and Crown Prince Mohammed bin Salman, to show the same level of sensitivity and release CCTV footage from the consulate".
The allegation that Khashoggi was killed in the consulate has been rejected by Saudi Arabia, which claims the dissident journalist left the premises alive.
Turkey's Foreign Ministry said Tuesday authorities would search the Saudi consulate, but there have been no details about when such a search would take place. He served as an adviser to senior Saudi officials.