Saudi Arabia's Crown Prince Abdullah has warned Muslim militants they will share the fate of al-Qaeda's chief in the kingdom unless they repent.
Abdul Aziz al-Muqrin was one of four militants shot dead in the capital, Riyadh, yesterday.
The Saudi government said the organisation in the kingdom has been weakened, but al-Qaeda has said its resolve remains intact.
In a statement posted on an Islamist website, the group, which has admitted a number of recent attacks on Saudi targets and Westerners, said it would continue what it called its Holy War.
A Saudi spokesman in Washington, Adel al Jubair, said Muqrin had been involved in the killing of the Irish cameraman, Simon Cumbers, and the wounding of his BBC colleague.
He also said the militant was responsible for the beheading of the American engineer, Paul Johnson.
Mr Jubair said the Saudi people were outraged by the killing of Mr Johnson.