The protests came as the Iraqi government ordered the closure of a popular independent television channel, Al Sharqiya, for inciting sectarianism.
In other news, US forces killed six people during a raid on a house in Baghdad.
"I have no sympathy for Saddam, but his life is not worth the lives of innocents that die daily in Baghdad"
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US soldiers came under fire as they approached an suspected hideout of the al-Qaeda in Iraq group, the US military said in a statement on Monday.
"Coalition forces received heavy automatic fire and hand grenades from the top of several nearby buildings", it said.
One of the buildings belonged to Saleh al-Mutlaq, head of the National Dialogue Front, a Sunni political party, the military reported.
An Iraqi security official gave a different version, saying four civilians were killed in a firefight late on Sunday as a result of clashes between al-Mutlaq's guards and those of a Shia parliamentarian, Salama al-Khafaji.
He said the two groups clashed in the al-Jamel area of western Baghdad, after which US troops, including military helicopters, arrived to quell the fight.
Four members of a family were killed and two of al-Khafaji's guards wounded, he added.
In Al-Dawr, close to Saddam's home village of Awja where he was buried on Sunday, hundreds of his supporters gathered.
In the nearby town of Tikrit, a bastion of Saddam supporters, dozens of mourning tents were erected for the late leader and the town was sealed off for a third straight day by security forces fearful of reprisal attacks.
|Palestinians in the West Bank protested|
against Saddam's execution [AFP]
Men, women and children sat in queues facing each other in the tents as volunteers served out the bitter black coffee customary during mourning.
The execution was also denounced in neighbouring Jordan.
Raghad Hussein, Saddam's eldest daughter, told protesters in Amman: "God bless you! I thank you for honouring Saddam the martyr."
Saddam was hanged at dawn on Saturday for his role in the killing of 148 Shia civilians after an assassination attempt against him in 1982 in the town of Dujail.
Footage of his final minutes showed him being taunted by his executioners, who chanted the name of Shia leaders before hanging him.
The Iraqi government has launched an inquiry into how guards filmed and taunted Saddam on the gallows, turning his execution into a televised spectacle that has inflamed sectarian anger.
Al-Sharqiya TV became on Monday the latest channel to incur the wrath of the Iraqi government. Brigadier Abdul Karim Khalaf, an interior ministry spokesman, said the government had ordered the channel to close indefinitely.
"We have warned them many times not to broadcast any false news that would increase tension in Iraq," he said, declining to specify which particular reports were false.
Owned by a London-based Iraqi businessman, the channel says it takes an independent editorial line, though many viewers see it as leaning towards a Sunni Arab viewpoint.
Al-Sharqiya was still broadcasting on Monday, as it broadcasts from Dubai, and it was not immediately clear what impact the government's order would have.