The shooting in the early hours of Saturday morning between police and armed men, who were firing from moving cars, came nearly a week after a major attack in the world’s biggest oil-exporting country killed 22 people in the city of Khobar.
An Islamist website claimed the al-Khobar attack on behalf of the al-Qaida network led by Saudi-born Usama bin Ladin.
“Police are currently pursuing a number of cars,” one source said. “They are trying to surround them.”
Fears about the security situation in the world’s biggest oil exporter helped push world oil prices to record highs last week before oil producers pledged to hike production.
On Friday, an alleged al-Qaida leader in the kingdom, Abd al-Aziz al-Muqrin, called on Saudis to support the the organisation’s campaign to topple the US-allied Saudi monarchy.
He praised an attack in the Saudi city of Yanbu in early May, the killing of a German in Riyadh two weeks ago and Wednesday’s shooting on US military personnel near Riyadh.
He also rejected a Saudi claim that two men killed near the western city of Ta’if on Wednesday had links to the Khobar attack.
Saudi Arabia has been fighting a low level insurgency for over a year and Muqrin has vowed 2004 will be “bloody and miserable” for the kingdom.