"Security forces gave chase to a car carrying three suspected militants in al-Rawdah neighbourhood and exchanged fire with the suspects. One of the gunmen was killed and another wounded," a witness told AFP on Monday.
The fate of the third suspect was not immediately known.
"The chase began around 6pm (15:00 GMT). Security patrols tried to stop the car at a crossroads and an exchange of fire ensued," the witness said.
Ambulances were seen in the area, but it was not known if there were casualties among the security personnel.
The witnesses said security forces cordoned off the area, while the siege continued for more than two hours.
It was not immediately possible to establish whether any of the suspected armed fighters were on a most-wanted list, as some witnesses claimed.
That list has gone down from 26 to 22 since it was issued by
authorities last December after a series of bombings in Riyadh that killed 52 people in May and November 2003.
Several suspects, as well as security personnel, have been killed in similar shootouts, particularly in the capital, since the attacks on residential compounds began.
"The chase began around 6pm (15:00 GMT). Security patrols tried to stop the car at a crossroads in the district and an exchange of fire ensued"
In the previous incident on 15 March, a Yemeni described as
al-Qaida's head of operations for Saudi Arabia and the rest of the Gulf, was killed in Riyadh.
Khalid Ali bin Haj, who ranked third on the most-wanted list,
was suspected of having ordered the Riyadh attacks, which had been blamed on al-Qaida sympathisers, according to Saudi security sources.
Two others on the most-wanted list had been killed in clashes with security forces while a third surrendered to authorities.