Iraqi officials have sought to calm fears that the new constitution will be delayed by the killing of three Sunni Muslims helping to draft the document.
Three Sunnis were gunned down for their part in the constitution
Four members of the drafting committee have temporarily quit in protest at the murders, voicing security concerns.
But the head of the drafting team said the document would be presented to the national assembly in the first week of August, well before the deadline.
MPs will then debate it and submit any changes ahead of a vote on 15 August.
"A draft will be presented to the national assembly in the first week of August," said Sheikh Humam Hammoudi, head of the drafting team.
The committee drafting the constitution was enlarged in July to include more people from the Sunni minority, amid fears they were rejecting politics for the insurgency.
However, on Tuesday gunmen killed a Sunni Muslim member of the committee and and two other Sunni politicians as they left a restaurant in central Baghdad.
New constitution to be completed by 15 August
National referendum on constitution by mid-October
Full government elections by mid-December
The militants have warned they will kill any Sunni Muslims working on the new constitution.
In response to the killings, four other members of the committee have refused to continue their work on the draft, voicing concern about the general lack of security.
But Sheikh Humam Hammoudi said he was pursuing ways to improve security for the committee members so they could safely return to work.
He insisted that despite the setback, work was progressing on schedule.
"After it is discussed by the national assembly and final changes are made, five million copies will be distributed to households... on August 15," he said.
Iraq is reeling from a devastating surge in shootings and suicide bomb attacks in recent weeks.
More than 100 have been killed in a blitz of attacks in recent days
On Wednesday the country's parliament held a three-minute silence at noon for those killed in two of the worst attacks in recent days.
The first incident involved the killing of more than 20 children in Baghdad a week ago, when US soldiers, who were giving them sweets, were targeted by a suicide car bomber.
And, in the second, at least 58 people were killed in an explosion in a petrol tanker near a Shia mosque in Musayyib, some 60 km (40 miles) south of Baghdad, on Saturday.
In the latest violence a suicide bomber has killed at least eight people and wounded many others at an army recruitment centre in Baghdad, say Iraqi police.
The attacker apparently mingled with the recruits before detonating his explosives belt at Muthanna airbase.
The abandoned airfield serves as an army recruitment centre and has been repeatedly attacked by insurgents.
The attack on the Muthanna centre recruitment centre happened at 0930 (0530 GMT) local time as young men were waiting to sign up to the military.
With mass unemployment in Iraq, there seems to be no shortage of recruits to the security forces, despite the dangers, says the BBC's Caroline Hawley in Baghdad.
In other developments, nine people working for the Iraqi tribunal set up to try Saddam Hussein have been dismissed for having links with his Baath party.
A spokesman for Deputy Prime Minister Ahmed Chalabi said the delay in putting the former Iraqi leader on trial so far was due to the presence on the tribunal of former Baathists.
On Sunday, Raed Juhi, the chief investigative judge, said a date for Saddam Hussein's trial would be set in the next few days.