The official said the clashes took place in Baghdad's suburb of Sadr City overnight.
The violence came as talks between the Iraqi interim government and al-Sadr's aides, which are aimed at ending violence in Sadr City, were stalled over the al-Mahdi Army's stockpile of weapons.
Sadr City police chief Colonel Maaruf Alami said a ten-point road map drafted by National Security Adviser Muwaffaq al-Rubaiay had been delivered to al-Sadr's office on Monday.
"The talks are stumbling on the final point," which urges the
rebel militia to hand over its weapons, Alami said.
The document calls for a seven-day truce and states that US troops should stop cracking down on al-Sadr's fighters and enter the sprawling neighbourhood only for reconstruction purposes.
It also demands the al-Mahdi Army stop attacking US bases, as well as Iraqi security forces and translators.
The ten points also include a commitment to rebuild the
Sadr City is an impoverished
suburb of Baghdad
impoverished neighbourhood and compensate residents who have been affected by months of fighting.
It adds that the Iraqi police will be responsible for conducting patrols in the area.
The talks come three days after the end of a bloody confrontation between the al-Mahdi Army and US troops in Najaf.
Interim Prime Minister Iyad Allawi has vowed to crush any fighters who refuse to disarm after top Shia cleric Grand Ayat Allah Ali al-Sistani secured the withdrawal of al-Sadr's fighters from the central shrine towns of Najaf and Kufa.