US President Donald Trump has suggested "rogue killers" could be behind the disappearance of Saudi journalist Jamal Khashoggi in Turkey.
Speaking to reporters after a phone call with King Salman, he said the Saudi leader had firmly denied knowing what had happened to Khashoggi.
Secretary of State Mike Pompeo is flying to Saudi Arabia immediately.
Saudi and Turkish investigators have been seen entering the Saudi consulate where Khashoggi was last seen.
Turkish officials believe Khashoggi was murdered in the consulate by Saudi agents nearly two weeks ago but Riyadh has always strongly denied this.
The issue has strained Saudi Arabia's ties with its closest Western allies.
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?"
The president provided no evidence to back his comment.
A Turkish security source has told the BBC that officials have audio and video evidence proving Khashoggi was murdered inside the building.
On Saturday, Trump threatened Saudi Arabia with "severe punishment" if it emerged that Khashoggi had been killed inside the consulate but ruled out halting big military contracts with Riyadh.
How are the Saudis reacting?
Diplomatic pressure is growing on the Saudis to give a fuller explanation.
On Monday, 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," an official quoted by Reuters news agency 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 Khashoggi's disappearance.
On Sunday, Riyadh angrily rejected political and economic "threats" over the case of the missing journalist and said it would respond to any punitive action "with a bigger one".
What do we know about the consulate search?
Investigators have been arriving at the building in Istanbul - first a Saudi team followed 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.
King Salman and Turkish President Recep Tayyip Erdogan spoke by telephone on Sunday evening, officials said, and stressed the importance of the two countries working together on the case.
What allegedly happened in Istanbul?
Khashoggi, a critic of the Saudi government who has written for the Washington Post, was last seen walking into the consulate on 2 October.
Reports suggest an assault and struggle took place in the consulate after Khashoggi went to get paperwork for his forthcoming marriage.
Turkish sources allege he was killed by a 15-strong team of Saudi agents but Riyadh insists that he left the consulate unharmed.
Khashoggi was once an adviser to the Saudi royal family but fell out of favour with the Saudi government and went into self-imposed exile. He is a US resident.
What other reaction has there been?
The European Union has joined calls for a transparent investigation.
EU foreign policy chief Federica Mogherini briefed reporters after a meeting of the 28 foreign ministers.
"There was full consensus around the table on the fact that we expect transparency, we expect full clarity from investigations to be done by the Saudi authorities together and in full co-operation with the Turkish authorities," she said.
Meanwhile, more leading business figures say they will not attend a major investment conference in Riyadh later this month.
The international conference, starting on 23 October, has been dubbed "Davos in the Desert", though the World Economic Forum says it has nothing to do with its annual event in the Swiss Alps.
Officially entitled the Future Finance Initiative, the Saudi conference describes itself as an "international platform for expert-led debate between investors, innovators and governments as well as economic leaders".
Significantly, it was expected to showcase the reform agenda of Saudi Crown Prince Mohammed bin Salman.
The head of JP Morgan, Jamie Dimon, is one of the latest high-profile executives to pull out.
Ford chairman Bill Ford and Uber chief executive Dara Khosrowshahi are also among those who will not be attending the conference.
A page with a list of confirmed speakers has been deleted from the event's website.
It is still unclear whether US Treasury Secretary Steve Mnuchin will attend the conference. A Treasury spokesperson told the BBC they would "be evaluating the information that comes out this week".