In a message to Crown Prince Mohammed bin Nayef, Saudi Arabia's interior minister, the king said he was "pained by the enormity of the crime", and pledged to hold those responsible for the attack to account.
"Every participant, planner, supporter, collaborator or sympathiser with this heinous crime will be held accountable, tried and punished," King Salman said in his message, reported on Sunday.
"Our efforts will never stop ... fighting the deviant thought, confronting the terrorists and wiping out their hotbeds."
The attack occurred at a mosque in al-Qadeeh in Saudi Arabia's heavily Shia east. Twenty-one people were killed and more than 80 wounded when a Sunni Muslim militant blew himself up during Friday prayers at the mosque in one of the worst attacks the kingdom has seen in recent years.
Isis, the militant organisation that has taken over large areas of Iraq and Syria, has claimed the attack, saying a new branch or the group was behind the Saudi bombing.
Saudi Arabia's interior ministry identified the bomber as Saleh bin Abdulrahman al-Qashaami, a Saudi citizen and acknowledged a link to Isis.
According to Bassam al-Attiyeh, an interior ministry spokesman, an unidentified subordinate of Abu Bakr al-Baghdadi, the Isis leader, communicated with five Saudi men in the same cell as al-Qashaami. All the men were now in custody, he said.
"We're talking about a terrorist infrastructure, we're talking about a very broad organisation that operates within the country," al-Attiyeh told the media.
"This organisation starts with Abu Bakr al-Baghdadi and under him the suspect whom we've mentioned, and one grade below him their combat and bombing wing ... under which is the killings and assassinations wing which undertook the al-Qadeeh incident."
Saudi Arabia is part of an international coalition carrying out air raids on Isis targets in Iraq and Syria. Isis has threatened to launch revenge attacks.
King Salman's comments on the al-Qadeeh mosque attack are seen as a conciliatory move at a time of increasing tensions between Sunnis and Shias in the region.