The Badr Brigades attacked a house in Najaf owned by a former official of the Baath party on Monday in retaliation for the bombings which killed, among dozens of others, Ayat Allah Muhammad al-Hakim.
A police officer said the assault took place at 05:00 (01:00 GMT) when members of the Supreme Assembly for the Islamic Revolution in Iraq (SAIRI) sought to kill Karim Ghaith, in al-Ishtiraki district in the south of the city.
Ghaith escaped the attack although his house was eventually burnt down, but two of the assailants died in the assault, according to the police official.
Badr Brigades militia leader, Sayyid Ali, had warned on Sunday that the “Americans cannot give us security. It is the Iraqis who must do this and the Badr Brigades are Iraqi. This is their right.”
Police chief shot
In a separate incident, Kufa police chief, Karim Attiyah, was shot in the right arm early on Monday morning as he drove through a checkpoint at the entrance to the Shia-majority city.
"He did not stop at a roadblock built by members of a political faction at the entrance to Najaf and they opened fire. He was wounded and taken to Najaf hospital," said a police officer refused to say if this was a Badr Brigades shooting.
On Sunday, bodyguards of Shia cleric Muqtada Sadr, who fiercely opposes the US occupation, opened fire on a car at a checkpoint, killing two people and wounding two others, hospital sources said.
"Americans cannot give us security. It is the Iraqis who must do this and the Badr Brigades are Iraqi"
Badr Brigades leader
Tensions are high in the city ahead of Tuesday's burial of SAIRI leader Ayat Allah Muhammad al-Hakim.
Al-Hakim’s remains will be taken around the city of Karbala before his corpse is returned to Najaf for burial on Tuesday.
Al-Hakim had lived in Iran in exile for the last 23 years.
He was killed in Najaf when two cars exploded outside the mausoleum of Imam Ali, leaving at least 82 people dead and more than 100 injured on Friday.
Iraqi police said they arrested a man on the Saudi border in connection with the attack, bringing to 19 the number of those detained after the blast.
Two Saudis believed to have ties to al-Qaida network have confessed to the attack, said local authorities.
Following the arrest of the two Saudis, the top Shia religious authority in Iraq, known as the Hawza, issued a warning that if the motive of the attack was sectarian there would be “dire consequences”.