Witnesses said on Friday that the three were gunned down during a clash in al-Malaz district in the centre of the Saudi capital - in what has become a bloody day for the kingdom.
The fighting broke out shortly after al-Qaida announced the execution of US citizen Paul Johnson.
Residents said one of the dead fighters was believed to be a top wanted Saudi dissident.
Unclear if Johnson's body found
Shortly earlier, an AFP correspondent saw dozens of security men deployed in al-Munisiyah neighbourhood in eastern Riyadh amid reports that the body of American aeronautics engineer Paul Johnson had been dumped there. But no body was found.
"Al-Qaida in the Arabian Peninsula" on Friday night posted gruesome pictures on Islamist web sites showing a beheaded Johnson, with his head placed on his back as he lay in a pool of blood.
Security forces also cordoned off two locations in the al-Rawdah neighbourhood in the eastern sector of the capital on Friday night.