Khadim Sarhid Ali al-Batawi was the leader of the Sunni Batta tribe and the brother of a candidate in the 15 December election, Maj. Falah al-Mohammedawi said.
The attackers were in Iraqi army uniforms and arrived at al-Batawi's home driving 10 cars of the same kind used by the Iraqi army.
One of al-Batawi's brothers said the family had been attacked earlier.
"A group of gunmen with Iraqi army uniforms and vehicles broke into my brother's house in the Hurriyah area and sprayed them with machine gunfire, killing him along with three sons and his son-in law," said his brother, Nima Sarhid Al-Hemaiyem.
"His eldest son was assassinated one month ago in the Taji area, northern Baghdad, when unidentified men shot and killed him."
Al-Mohammedawi said government forces were not involved in the slaying and that the investigation was focused on anti-US fighters.
The family had been attacked
earlier, said al-Batawi's brother
"Surely, they are outlaw insurgents. As for the military uniform, they can be bought from many shops in Baghdad," he said. "Also, we have several police and army vehicles stolen and they can be used in the raids."
One of al-Hemaiyem's sons was a police officer, the other had recently quit the force. The Batta tribe is from the area north of Baghdad, where they are influential.
Dozens of people went to al-Hemaiyem's home, where the bodies were laid out, wrapped in blankets before the funeral.
The slaying follows a big push by US officials to encourage Sunni Muslim participation in the 15 December election, which will install the first non-transitional government in Iraq since the 2003 invasion.
Some Sunni-led groups which oppose the US military presence in Iraq, have declared a boycott of the election and have threatened politicians who choose to participate in it.
The Association of Muslim Scholars, a Sunni organisation, called the slaying "cowardly" and also condemned the killing of a Sunni cleric and his brother in Khan Bani Saad, a town 30 km northeast of Baghdad.
Reading from a statement, association spokesman Abdul Salam al-Kubaisi said Iraqi soldiers had arrested the two men two hours before they were found dead, suggesting they might have been involved.
"We warn the government against continuing with this tyranny," he said.
Meanwhile, in the mostly Shia neighbourhood of Sadr City in Baghdad, a group of armed men blocked the road leading to the Communist Party's branch office on Tuesday afternoon just after the party began its election campaign, a statement said.
Talabani says he is ready for
talks with the armed opposition
The unidentified men broke into the party building and killed two activists in the reception area, it added.
"This cowardly act coincides with our preparations for the upcoming election and it targets the political process," the party said. "The government should bear the responsibility of providing the necessary protection in order to ensure a safe atmosphere for the elections."
In another development, US and Iraqi troops launched an operation in predominately-Sunni western Iraq on Tuesday to prevent Iraqi fighters from stopping the vote in that city, a US military statement said.
The operation in Ramadi, 115 km west of Baghdad, is the third in the city since 16 November. The operations have resulted in 32 enemy killed, and the seizure and destruction of surface-to-air missiles, rocket-propelled grenades, mortar rounds, artillery rounds, hand grenades, small arms and bomb making equipment, the statement said.
In Baghdad, a US official close to the trial of Saddam Hussein said the court expects defence lawyers to attend next week's hearing, despite their threat to boycott the trial.
The official told a news briefing that the court has "standby" defence lawyers to step in if the defence team makes good on its threat to boycott the 28 November hearing, the first since the trial opened on 19 October.
The threat followed the assassination of two members of the defence team since 19 October. They have since demanded protection for themselves and their families, as well as a UN investigation into the killings.
In a positive development, a senior government official said a representative of an unidentified resistance group responded to an offer by President Jalal Talabani to talk with those willing to lay down their arms.
Presidential adviser Lt. Gen. Wafiq al-Samaraei told Aljazeera that he had received a call from someone "who claimed to be a senior official of the resistance".
"I have received a message from a person who claims he is linked to the Iraqi resistance. I have immediately welcomed his call since listening to others' views does not mean that you should accede to their demands and accept their strategy.
Saddam defence team will
attend the trial on 15 December
"It is imperative for the president of the republic to listen to all the citizens, be they good people, suspects or even criminals. This is my genuine understanding of this matter, away from false language," al-Samarraei said.
Al-Samaraei, a former head of military intelligence under Saddam, did not identify the caller, and it was unclear whether the overture represented a breakthrough.
However, Shia government officials blasted the Sunni-led revolt, saying a legitimate resistance movement should not kill civilians or destroy its own country.
"We are tired of the slogans that call for the departure of the British and the Americans," Prime Minister Ibrahim al-Jaafari said during a seminar on an anti-terrorism law passed last month.
"We are now under the umbrella of the United Nations. ... we should all work for tolerance and to strangle terrorism."