He said the Saudi king had firmly denied knowing what had happened to Jamal Khashoggi.
Secretary of State Mike Pompeo is flying to Saudi Arabia immediately.
Turkish police have, for the first time, been inside the Saudi consulate where Jamal Khashoggi was last seen.
They entered the building around an hour after a group of Saudi officials.
Turkish officials believe Jamal Khashoggi was murdered in the consulate by Saudi agents nearly two weeks ago but Riyadh has always strongly denied this.
Meanwhile, unconfirmed media reports suggest Saudi Arabia is preparing to admit that Jamal Khashoggi died as a result of an interrogation that went wrong and that the original intention had been to abduct him.
Arabic channel Al-Jazeera quotes Turkey’s attorney-general’s office as saying it has found evidence to back claims that Jamal Khashoggi was killed inside the mission.
The issue has strained Saudi Arabia’s ties with its closest Western allies.
President Trump addressed snatched questions from reporters over helicopter engine noise at the White House, describing King Salman’s denial as “very, very strong”.
“It sounded to me like maybe these could have been rogue killers,” he added.
“Who knows?”
President Trump provided no evidence to back his comment.
Last week, the president threatened Saudi Arabia with “severe punishment” if it emerged that Jamal Khashoggi had been killed inside the consulate but ruled out halting big military contracts with Riyadh.
Secretary of State Mike Pompeo’s visit to Saudi Arabia will be followed by a stop in Turkey.
Diplomatic pressure is growing on the Saudis to give a fuller explanation.
On October 15, King Salman ordered an investigation into the case.
“The king has ordered the public prosecutor to open an internal investigation into the Khashoggi matter based on the information from the joint team in Istanbul,” a Saudi official quoted by Reuters said.
The official said the prosecutor had been instructed to work quickly.
Last week, Turkey accepted a Saudi proposal to form a joint working group to investigate Jamal Khashoggi’s disappearance.
Investigators entered the consulate in Istanbul on October 15 – first a Saudi team followed roughly an hour later by Turkish forensic police.
Turkish diplomatic sources had said the consulate would be searched by a joint Turkish-Saudi team.
A group of cleaners was seen entering earlier.
Saudi Arabia agreed last week to allow Turkish officials to conduct a search but insisted it would only be a superficial “visual” inspection.
Turkey rejected that offer. The Sabah daily newspaper said investigators had wanted to search the building with luminol, a chemical which shows up any traces of blood. It is not clear whether that happened.
King Salman and Turkish President Recep Tayyip Erdogan spoke by telephone on October 14, officials said, and stressed the importance of the two countries working together on the case.
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