Trump said he spoke to the Saudi king for about 20 minutes about Khashoggi, who disappeared after entering the Saudi consulate in Istanbul on Oct 2, and that it sounded like neither the king nor Crown Prince Mohammed bin Salman had knowledge about the incident.
Turkish sources have said they believe Khashoggi was killed inside the building and his body removed, allegations that Riyadh dismisses as baseless.
"I sounded to me like maybe there could have been rogue killers. Who knows?" Trump told reporters at the White House. He offered no evidence for why he thought rogue killers might be involved.
Pompeo will travel to Riyadh, the US State Department said,
"The president has called for a prompt and open investigation into the disappearance of Washington Post journalist Jamal Khashoggi," department spokeswoman Heather Nauert said in a statement.
"We are going to leave nothing uncovered," Trump told reporters.
Salman's denial, however, "could not have been stronger," he added.
But Trump has said he is wary of halting US military sales to Saudi Arabia over the incident.
Earlier on Monday, Salman ordered an internal probe into Khashoggi's disappearance while a joint Turkish-Saudi team was set to search the consulate.
Trump said the king told him on Monday that the two countries were working very closely on the case.