Yet Mr Trump stopped short of threatening to ban arms deals with the Saudis, claiming such sanctions would only hurt jobs in the US defence industry.
The president revealed US authorities were now investigating the suspected torture and killing of Mr Khashoggi at the Saudi embassy in Turkey on 2 October.
“It’s being investigated, it’s being looked at very, very strongly,” he told CBS News in his first 60 Minutes interview since becoming president.
Mr Trump said the US would be “very upset and angry” if the Saudi authorities were found responsible.
“They deny it – they deny it every way you can imagine,” he added. “In the not too distant future I think we’ll know the answer.
“We’re going to get to the bottom of it and there will be severe punishment.”
Later, after welcoming freed pastor Andrew Brunson to the White House, the president said that his hopes that Mr Khashoggi was still alive were ”not looking too good”.
“Our first hope was that he was not killed but maybe that’s not looking too good from what we hear but there’s a lot to learn, there really is,” he told reporters.
Trump said that he would meet with Mr Khashoggi’s family but added that he had not yet discussed the case with Saudi King Salman.
He also appeared to rule out a ban on selling arms and military equipment to Saudi Arabia, adding: “I actually think we’d be punishing ourselves.”
The president said that the sale is a “tremendous order for our companies” and suggested that the kingdom would only purchase weapons from Russia or China.
“There are other things we can do that are very, very powerful, very strong and we’ll do them,” Mr Trump added.
A critic of the Saudi government, Mr Khashoggi went missing more than a week ago after he entered the Saudi consulate in Istanbul.
Turkish officials have said they believe the 59-year-old was murdered there by a 15-member Saudi “assassination squad”.
The Turkish newspaper Sabah has reported that the moments during which Mr Khashoggi was allegedly tortured and killed may have been recorded by his Apple Watch.
Senior Turkish officials previously told Reuters Mr Khashoggi had been wearing an Apple Watch when he entered the consulate, and claimed it had been connected to a mobile phone he left outside the building.
It follows reports that US intelligence officials have already seen video and audio recordings of the murder.
On Friday, a delegation from Saudi Arabia arrived in Turkey as part of the investigation into the reporter’s disappearance.
The Turkish foreign ministry said the Saudi consulate in Istanbul would be searched as part of the probe.
Mr Khashoggi, a critic of the Saudi authorities, had reportedly been banned from writing in newspapers, making TV appearances or attending conferences in Saudi Arabia after he criticised Mr Trump following his election victory in 2016.
Join our commenting forum
Join thought-provoking conversations, follow other Independent readers and see their replies