The militants were said to be members of the Islamic State of Iraq and the Levant (ISIL), a jihadi group also fighting in Syria.
ISIL militants and other Sunni groups angered by the Shi'ite-led government overran Fallujah and parts of the nearby city of Ramadi in the western province of Anbar last month.
Prime Minister Nuri al-Maliki has held back from an all-out assault on Fallujah to give time for a negotiated way out of the standoff, but mediation efforts appear to have failed.
Troops intensified shelling of Fallujah late on Sunday and security officials said a ground assault would follow soon.
Mr Maliki has appealed for international support and weapons to fight al Qaeda, although critics say his own policies towards Iraq's once-dominant Sunni community are at least partly to blame for reviving the insurgency.