Thursday's attack followed two bombings in May of mosques used by the kingdom's Shia Muslim minority that killed 25, several shootings of policemen in Riyadh and a car bomb outside a prison in the capital in July, all claimed by Islamic State.
The terrorist movement regards Riyadh's ruling family as having betrayed Islam through its close ties with the West, and wants to replace all Muslim states, including Saudi Arabia, with a single caliphate.
"His Highness Prince Mohammed bin Nayef bin Abdulaziz called on the need to intensify preparedness and raise the level of caution in the face of any developments that, God forbid, may arise," the official Saudi Press Agency reported. The crown prince is also interior minister.
Read: At least 13 killed in bomb attack on Saudi mosque
Islamic State's leader Abu Bakr al-Baghdadi called last year for supporters in Saudi Arabia to launch their own attacks on Shias, government targets and Westerners instead of travelling to Iraq or Syria to join his group.
Read: Pakistan condemns terrorist attack at Saudi mosque
Saudi Arabia has joined the US and other Arab states in airstrikes against the group in Syria, has mobilised state-affiliated clergy to denounce the group and has detained hundreds of its suspected supporters.
Thursday's blast took place during noon prayers at the mosque in the Special Emergency Forces Centre in Abha, the capital of the southwestern Asir province, killing five members of the force, six trainees and four Bangladeshi workers.
Islamic State claimed responsibility for attacking what it called "a military camp" on Thursday and the Interior Ministry on Saturday named the bomber as 21-year-old Saudi national Yousef bin Sulaiman Abdullah al-Sulaiman.
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