The National Assembly only approved a final text of the constitution on Sunday, giving little time for the United Nations to print five million copies and distribute them nationwide ahead of the referendum.
Hussein al-Shahristani, the deputy speaker of parliament, told reporters it was an absolute final draft of the text, which has been held up repeatedly by last-minute amendments.
"There is no way there will be any changes now," he said. "The draft is being submitted to the United Nations and will be presented to the Iraqi people soon."
Hours before the draft was approved, Kurdish parliamentary deputy Faris Naser Husain was shot dead along with three bodyguards as he travelled to Baghdad from the north.
Fellow deputy Haider Qassem was also wounded, National Assembly spokesman Peshro Saeed said.
The shooting as well as a car bomb that killed 30 people in Baghdad on Saturday came after a week of carnage that saw 250 people killed in the capital and elsewhere.
The Kurdish- and Shia-led government, backed by US forces, is facing a Sunni Arab uprising aimed at bringing it down, and the US military has said it expects violence to rise before the 15 October constitutional referendum.
Twenty bodies found
Also on Sunday, the bodies of 20 men, apparently members of the Iraqi security forces, were found in the Tigris river north of Baghdad, according to the security services.
The men had their hands tied and were executed by gunshots, according to the defence ministry, which said the bodies were found near the village of Balad.
An Interior Ministry source confirmed that the bodies of 20 men had been found, but could not confirm if they had been members of the security forces.
Sunni Arabs, who dominated Iraq under former president Saddam Hussein, fear the charter will formalise the loss of influence they have endured since he fell and boost the autonomy of southern Shia in line with that already enjoyed by northern Kurds.
Many Sunnis have said they will reject it. And in an internet statement last week, Abu Musab al-Zarqawi, the leader of al-Qaida in Iraq, purportedly called for a war against Shia following an Iraqi-led, US-backed military assault on the northern town of Tal Afar.
Abu Musab al-Zarqawi has called
for war on Iraq's Shia
Baghdad and Washington said Tal Afar was a stronghold of "terrorists and foreign fighters", and blamed al-Zarqawi for the bomb attacks and shootings across Baghdad last week.
Shia leaders led by populist cleric Muqtada al-Sadr urged Sunnis on Sunday to take a tough stand against rebels in the face of al-Zarqawi's declaration of war.
Al-Sadr spokesman Abd al-Hadi al-Darraji said the influential Association of Muslim Scholars should take more decisive action against those inciting civil war.
"We want them to issue a fatwa (religious edict) forbidding Muslims from joining these groups that deem others infidels," he said. "This will be crucial in ending terrorism."
Tensions are also high ahead of the 19 October trial of Saddam on a single charge of mass killing in reprisal for an assassination attempt in 1982.
The attempt on his life was made in Dujail, the village where Kurdish deputy Faris Naser Husain was also shot on Saturday.
US soldier killed
A US soldier was killed by a bomb explosion on Saturday near al-Asad, in western Iraq, the US military said in a statement on Sunday.
His death brings to at least 1899 the number of American military personnel killed in Iraq since the US-led invasion of March 2003, according to Pentagon figures.
The death comes as Iraqi Prime Minister Ibrahim al-Jaafari told the UN General Assembly in New York that it was not time for the departure of US-led forces from the country.
Soldiers taken captive
Meanwhile, Aljazeera learned that unidentified fighters are believed to have taken 15 Iraqi soldiers hostage west of Samara.
Aljazeera also learned that the al-Qaida leader in Mosul, Junaid Farhat, was killed in a US air strike along with four of his men.