One policeman was injured and officers were also chasing a second car, the source said. The clash on Friday came just hours after three other insurgents were killed in a gunbattle with police in the city overnight.
Saudi Arabia is battling a wave of violence linked to disaffected Islamists who are also blamed for bombings that killed at least 50 people in Riyadh last year.
Many dissidents, as well as security personnel, have been killed in gunbattles in the past year, and hundreds more presumed Islamist dissidents have been rounded up across the vast kingdom.
The latest incidents came close on the heels of Wednesday's car bomb which targeted a security forces building in Riyadh, killing at least five people and wounding 145 others.
A suspected dissident is arrested
The bombing drew renewed pledges from authorities to crush dissidents as a group claimed responsibility for the attack and threatened more in future.
"These criminal acts perpetrated by a deviant minority will be dealt with firmly until they are rooted out," Crown Prince Abd Allah bin Abd al-Aziz said after the blast, the first to target an official building since the wave of bombings began nearly a year ago.
Twenty children were among the wounded, who included Saudis and mainly Arab expatriates, Africans and Asians.
The Al-Watan newspaper said the bombing revealed the spuriousness of slogans by Islamists and al-Qaida supporters who "previously justified terrorism by (wanting to) expel the non-believers from the Arabian Peninsula."
"Our wounds can only be healed by jihad"
Brigades of the Two Holy Mosques in the Arabian Peninsula
"Now they are aiming their acts of treason against the defenders of the security of the nation... who are all Muslim citizens."
Grand mufti Shaikh Abd al-Aziz al-Shaikh, the country's highest state-appointed religious authority, said the attack flouted Islamic teachings and was carried out by "a lost minority under the cover of religion."
In claiming the attack a group calling itself "Brigades of the Two Holy Mosques in the Arabian Peninsula" said it had "succeeded in blowing up the headquarters of the special security and anti-terrorism forces related to the interior ministry."
The group, which has made similar claims in the past, said it "will not forget the blood of the martyrs" in the "anti-terror" hunt by Saudi security forces.
"Our wounds can only be healed by jihad," added the statement posted on an Islamist website but whose authenticity could not be verified.