They said at least two other people were wounded in Wednesday’s gunfight, but it was not immediately clear if they were policemen or gunmen.
Police were surrounding the al-Quds area of Riyadh and helicopters hovered overhead, a reporter said.
One of the two dissidents was near the top of the kingdom’s most-wanted list, police said.
Abd Allah Muhammad Rashid al-Rashud was “one of the most dangerous suspects in the kingdom” and was on the government’s list of most wanted people, the source said.
Saudi Arabia, the world’s biggest oil exporter, has been battling a year-long wave of attacks by al-Qaida-linked insurgents who are committed to toppling the pro-US monarchy.
Bringing down the Saudi monarch
Earlier this month, security forces killed the leader of al-Qaida in the kingdom along with three other senior fighters. The Saudi wing of Usama bin Ladin’s network has since named
Salah al-Awfi as the new leader of the group.
At least 85 policemen and civilians, many of them foreigners, have been killed in the shootings and bombings blamed on al-Qaida.
Last week, Saudi Arabia’s de facto ruler, Crown Prince Abd Allah, announced a limited government amnesty for dissidents who surrender, but said the families of their victims could press for punishment.
But al-Qaida-linked websites predicted the amnesty offered would fail, the group said in its military publication Muwaskar al-Battar.
In al-Qaida’s bloodiest attack in the kingdom so far, 22 civilians were killed last month in the eastern oil city of Khobar after a shooting and hostage-taking spree.
The United States and Britain, key allies of Saudi Arabia, have urged their 65,000 citizens in the kingdom to leave, citing the possibility of further attacks.