The clashes came after the city was rocked by twin car-bombings that left two people dead and injured 100.
Wednesday's bomb attacks in the oil-rich kingdom, which has been battling a wave of opposition unrest since May last year, prompted security alerts elsewhere in the Gulf region and sent world oil prices rising.
The opposition fighters struck at the heart of the Saudi government's security apparatus, targeting the interior ministry and a special forces base in Riyadh.
"It is clear now that their aim is not confined to fighting 'infidels' as they claim, but also ... to destabilise security through killing Muslims and harming peaceful citizens," Deputy Interior Minister Prince Ahmad bin Abd al-Aziz said during a visit to the site of the ministry blast.
A Pakistani taxi driver and a Saudi security man were killed in
the attack on the ministry building, the Al-Iqtissadiya newspaper said.
Human remains found
The interior ministry said six guards were wounded in the attack on its offices, along with several bystanders, and that foreigners were among the wounded in the second explosion at the special forces base in eastern Riyadh.
Ministry spokesman Mansur al-Turki said both attacks appeared to have been "suicide" operations, as human remains were found inside the vehicles.
In the first attack, the bomber rammed the gate of the ministry compound, triggering a shootout with guards before the vehicle blew up, witnesses said.
"It is clear now that their aim is not confined to fighting 'infidels' as they claim, but also ... to destabilise security
through killing Muslims and harming peaceful citizens"
Prince Ahmad bin Abd al-Aziz
Deputy Interior Minister
In the second, guards at the special forces base intercepted the vehicle before it reached the gate, forcing the bomber to detonate his charge more than 350m away, the ministry said.
Saudi forces killed a total of 10 opposition fighters in gun battles on both Tuesday and Wednesday, state television said on Thursday.
They included two of the kingdom's most wanted men - Saudi nationals Sultan Bjad Saadun al-Utaibi and Bandar Abd al-Rahman al-Dakhil.
Yemeni national Ibrahim Ahmad Abd al-Majid al-Reemi, believed to have been an intermediary between al-Qaida leader Usama bin Ladin and fighters loyal to him in the kingdom, was also among the dead.
Saudi Arabia has been swept by a wave of opposition attacks since May 2003, much of it directed against foreigners, which the authorities blame on the al-Qaida network.
Opponents of the ruling House of Saud say it is dictatorial and corrupt.
Bin Ladin has encouraged attacks
against the ruling House of Saud
In response, the Saudi government accuses its opponents of "terrorism" and the desire to provoke instability in the country.
More than 100 people have died in the ongoing confrontations and hundreds more have been wounded.
The latest violence came shortly after the airing of a
purported voice message from bin Ladin urging his followers to rise up against the Riyadh government and attack oil sites in Saudi Arabia and the Gulf.
On Wednesday, the US embassy had again urged nationals in the kingdom to exercise extra caution.
Oil prices surged on news of the
latest bombings in Saudi Arabia
In neighbouring Kuwait, the authorities increased security around vital installations such as oil facilities and potential Western targets, security officials and witnesses said.
Units from the national guard and special forces were deployed around hotels, Western residential buildings and key installations as police set up checkpoints along roads.
Oil prices surged on news of the bombings, with New York's main crude oil contract shot higher by $1.87 to close at $43.64 on Wednesday before dropping back on Thursday.
Saudi Arabia is the world's number one oil producer and
exporter, and the only one with spare capacity to meet spikes in demand in consumer countries.