No one was wounded by Friday's roadside bomb outside the Iraqi Islamic Party office in Fadhal, a district of central Baghdad.
But the rare attack against the group by Sunni-led fighters appeared aimed at punishing it for deciding to end its "no" campaign against the referendum after lawmakers agreed on Wednesday night to several amendments to the constitution designed to win Sunni Muslim support in Saturday's vote.
On Thursday, banners of the Iraqi Islamic Party urging a "no" vote had been removed from where they hung near monuments such as the capital's main Grand Imam mosque.
"This attack by insurgents against the Islamic Party was expected because of its new stand towards the referendum," Iraqi army Major Salman Abdul Yahid said in an interview.
"Insurgents had threatened to attack the group and its leaders to get revenge."
Many Sunni Arab parties still oppose the charter.
The Iraqi Islamic Party no longer
urges Sunni Arabs to vote 'no'
They fear it would divide Iraq into three separate districts: powerful mini-states of Kurds in the north and Shia in the south, both capitalising on Iraq's oil wealth.
By contrast, many Sunni Arabs fear, their group would be left isolated in central and western Iraq with a weak central government in Baghdad.
On Wednesday night, the National Assembly endorsed last-minute changes to the draft constitution worked out by Shia, Kurdish and Sunni Arab power-brokers that will allow a new parliament scheduled to be elected in December to adopt amendments to the constitution.
The draft constitution now being considered by voters is expected to pass on Saturday. It requires a majority, and it will be adopted unless two-thirds of voters in three provinces vote "no". Sunni Arabs only have a majority in four of Iraq's 18 provinces.
Iraqis continued to prepare for the referendum on their draft constitution.
Interior Minister Bayan Banker Solagh announced a series of security measures before Saturday's vote, including a four-day national holiday through Sunday, a ban on civilians carrying weapons, and a new 10pm to 6am curfew.
Khalilzad: Successful referendum
may lead to US troop withdrawal
Iraq's borders have been closed , with only vehicles transporting food, water and fuel exempted.
For his part, US ambassador Zalmay Khalilzad said a successful referendum is a key component of US military withdrawal.
"Iraq's success is our exit strategy," said Khalilzad. US forces can leave the country "as soon as Iraq can stand on its own feet".
Khalilzad said the uprising could be defeated only through a joint military, political and economic strategy. "I believe strongly that you cannot defeat the insurgency through military means alone," he said.
US officials meanwhile gave contradictory assessments on the level of violence.
In Washington, US State Department deputy spokesman Adam Ereli said on Thursday that preparations for the vote were going "very well" and suggested the level of violence was lower than before the last elections in January.
Ereli was unable to give any figures to back up his assertion about the bloodshed, and under persistent questioning appeared to give ground.
"The number of attacks, in our view, is not the measure of the success or the strength of democracy in Iraq," he said.
And "I don't think anyone is under any illusion that the attacks are about to end or that we're turning an important corner", he added.
"The number of attacks, in our view, is not the measure of the success or the strength of democracy in Iraq"
US State Department deputy spokesman
However, in Baghdad, Major General Rick Lynch, spokesman for the US-led forces in Iraq, emphasised that the number of attacks has dropped compared to the period leading up to the January polls which elected the current legislature.
One reason he gave: US and Iraqi forces have killed or captured 91 people said to be leaders of Al-Qaida in Iraq. "We believe that decimating their leadership has had a significant impact on the number of attacks," he said.
Lynch added that US-led forces and Iraqi forces were nevertheless bracing for an increase in attacks linked to the referendum. Fighters "will do everything they can to derail the process," he said.
In Washington, a quarterly Pentagon report showed that as of 16 September, the number of attacks by Iraqi fighters was averaging nearly 600 per week, compared with just over 500 around the country's landmark parliamentary elections in January.
The constitution will be adopted if a simple majority of voters approve the text in Saturday's referendum and if two thirds of voters in three or more provinces do not reject it.
A total of 15.5 million Iraqis are registered to vote from the population of 26 million.