Trump also told reporters Saturday that there would be "very powerful" repercussions if Saudi Arabia is found to be responsible.
Khashoggi, who has lived in self-imposed exile in the US since a year ago to avoid possible arrest, has not been seen since entering the Saudi Consulate in Istanbul on October 2 and was reported missing by his Turkish fiancee.
Describing the disappearance as a "terrible thing", Trump said the United States would find out what happened to Khashoggi.
"So, we do that, we really are hurting our country a lot more than we're hurting Saudi Arabia".
As the controversy intensified, the Washington Post reported Turkish officials had recordings made from inside the building that allegedly proved their claims Khashoggi was tortured and killed at the consulate.
Saudi Arabia warned Sunday it would retaliate against any sanctions imposed on the oil-rich kingdom over the disappearance of journalist Jamal Khashoggi, as the Riyadh stock market plunged on growing investor jitters.
"None of us know what happened, but we are all extremely concerned about the stories that have emerged, and the country that can help us get to the bottom of this is Saudi Arabia", he added.
Khashoggi disappeared over a week ago while on a visit to the Saudi Consulate in Istanbul, sparking an global uproar involving the Kingdom, Turkey and the United States that remains unresolved.
NEW YORK - Ford Motor Co Chairman Bill Ford canceled a multi-stop trip to the Middle East, including a planned appearance at a Saudi investment conference, the company said on Sunday, the latest such cancellation after the disappearance of Saudi journalist Jamal Khashoggi.
Once an adviser to members of the royal family, Khashoggi fell out of favour for his criticism of Crown Prince Mohammed bin Salman's reform programme.
The fiancée of Jamal Khashoggi has said that she will only consider accepting Donald Trump's invitation to the White House if the United States president is prepared to make a "genuine contribution" to investigating the Saudi critic's disappearance.
In a statement by the Saudi Press Agency, the government denied any involvement: "The Kingdom affirms its total rejection of any threats and attempts to undermine it, whether by waving economic sanctions, using political pressure, or repeating false accusations".
Republican Marco Rubio of Florida says that includes the multi-billion dollar arms deal that President Donald Trump wants to preserve.
"If U.S. sanctions are imposed on Saudi Arabia, we will be facing an economic disaster that would rock the entire world", Aldakhil wrote on Sunday.
However, there is more pressure from the USA - traditionally and ally to Saudi Arabia - which has said it is considering boycotting a major global conference in to be held in the Kingdom later this month.
Oil prices could surge to all-time highs if the USA imposes economic sanctions against Saudi Arabia, according to an opinion piece written by the general manager of Saudi Arabia-based Al Arabiya television.