Trump said he didn't "want to get into (Salman's) mind", but told reporters: "it sounded to me like maybe these could have been rogue killers".
The comments marked a break from the Trump administration's previous refusal to speculate over the fate of Khashoggi and came as the United States president is under growing pressure to take action on the case.
Turkish authorities have told USA officials that they have recordings from inside the Saudi consulate in Istanbul that prove Khashoggi was killed inside, officials told NBC News.
Trump tweeted Monday that he had spoken with the Saudi king, "who denies any knowledge" of what happened to Khashoggi. Pompeo will "immediately" travel to meet the Saudi king, Trump wrote.
The report came hours after Turkish investigators entered the consulate for what officials called a joint inspection of the building where Khashoggi was last seen alive, entering the diplomatic post, almost two weeks ago.
Turkish government officials have said a team of Saudi agents killed and dismembered Khashoggi, who was last seen entering the Saudi Consulate in Istanbul on October 2.
Gianella Palet consiguió la medalla con Las Leoncitas — Mendocina de oro
Después, en los cruces fue lapidario: limpió a Namibia por 3-0 en los cuartos de final y a Sudáfrica por 11-0 en las semifinales. Es más, el hockey femenino, pese a todos los logros que acumularon, nunca tuvo a Las Leonas en lo más alto del podio olímpico.
But the president has also said "we would be punishing ourselves" by canceling arms sales to Saudi Arabia.
Kudlow said changing circumstances could still affect Mnuchin's decision.
The president provided no evidence to back his comment.
"He's intending to go because of the importance of the issue of ending terrorist financing", Kudlow said on ABC's "This Week." Rubio said US-Saudi relations may need to be "completely revised" and stressed the US would lose credibility on human rights if the Trump administration remained silent.
The ministry said the search would be carried out as part of the ongoing investigation by Turkish authorities regarding Khashoggi's fate. "I mean, who knows?" Saudi Arabia has denied the claims. Saudi Arabia is leading a coalition of Gulf states in a military campaign against Iranian-backed Houthi rebels in Yemen.
The Turkish government believes Khashoggi was killed and dismembered inside the consulate, and his body removed in suitcases or boxes. The writer had been living in self-exile in Virginia for the past year.
Sen. Bob Corker, Republican-Tennessee, who as chairman of the Senate Foreign Relations Committee has reviewed the USA intelligence into what happened to Khashoggi, has said, "The likelihood is he was killed on the day he walked into the consulate".
Writing for Al Arabiya yesterday, Mr Aldakhil said: "If US sanctions are imposed on Saudi Arabia, we will be facing an economic disaster that would rock the entire world".