United States and Saudi Arabian officials say Paul Johnson's beheaded body has not been found.
Spokesmen said at the weekend that they were searching the northern outskirts of Riyadh and desert areas around the capital.
Houses and apartments that security forces suspect were used by militants responsible for his kidnapping were being searched.
Security forces found the car carrying Abdulaziz al-Muqrin and his militant colleagues in al-Malaz neighbourhood. A gunbattle erupted in which Muqrin, responsible for Johnson's beheading, was killed.
Three other militants - Faisal Abdul-Rahman al-Dikheel, Turki bin Fuheid al-Muteiry and Ibrahim bin Abdullah al-Dreiham - were also killed, as was a security officer.
The Interior Ministry said 12 suspected militants were also arrested in a sweep of the capital.
The ministry said authorities had confiscated three cars used by Muqrin's cell, forged identity papers, US$38,000 ($61,000) and a weapons cache, including three rocket-propelled grenade launchers, hand grenades and automatic rifles.
Body of killed hostage missing
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