The US ambassador in Riyadh, James Oberwetter, has praised Saudi Arabia for last night's security operation in Riyadh in which a local al Qaeda leader, Abdulaziz al-Muqrin, was killed.
Saudi officials said al-Muqrin and three other militants were killed in a shootout after dumping the body of the American hostage Paul Johnson, who was beheaded hours earlier.
One of the dead men is said to have been involved in last month's incident in the Gulf oil city of Khobar, in which hostages were taken.
In a separate development, US Secretary of State Colin Powell has said the departure of American citizens from Saudi Arabia would be a victory for extremists there.
Mr Powell said he was confident that American corporations' heightened security measures would keep staff safe.
Earlier, the state department urged its citizens to leave the country.