Saudi Arabia warned terrorists they would share the fate of their slain leader unless they repented, as al Qaeda vowed renewed war in the kingdom.
Al Qaeda's leader in Saudi Arabia, Abdulaziz al-Muqrin, was shot dead by Saudi forces on Friday along with three others hours after they beheaded American hostage Paul Johnson, whose body has still not been found.
Saudi analysts who have contacts with terrorists said on Sunday they expected al Qaeda to name Saleh al-Awfi, a former Interior Ministry employee, as Muqrin's successor.
"We tell this deviant group and others that if they do not return to the right path, they will meet the same fate or worse," Saudi Arabia's de facto ruler Crown Prince Abdullah said late on Saturday.
"Security forces will deal with them, God willing, and with every aggressor inside or abroad," he added.
State television showed the bloodied corpses of the four terrorists, saying they had been behind a wave of violence against foreigners in the Gulf state.
"The government is strong and will eradicate the enemy and cleanse the country of them," Saudi Interior Minister Prince Nayef said. "God willing, we will be victorious."
Al Qaeda confirmed the killings of Muqrin and three others in an Internet statement on Saturday but voiced defiance.
Saudi foreign policy adviser Adel al-Jubeir said Riyadh would pursue extremists without mercy.