Thousands of Shias have marched in the southern Iraqi city of Basra to back the new constitution and to mourn 1,000 pilgrims who died in a stampede.
Shia demonstrators chanted 'Yes to the constitution'
Some Shia politicians back a federal region in the south, an idea allowed for in the constitution but opposed by many Sunnis.
Tensions have risen since the stampede at a Shia ceremony in Baghdad.
A girl was killed in a gun battle between Sunnis and Shias on Thursday near the scene of the tragedy.
Politicians were said to be discussing possible changes to the draft constitution to address Sunni concerns ahead of a referendum next month.
Shia negotiator Khalid al Attiyah told the Associated Press they were looking at three to four unidentified clauses that might help the constitution win approval in the 15 October vote.
The rally in Basra was organised by the powerful Shia Supreme Council for Islamic Revolution in Iraq, and was one of the first in support of the constitution.
"Yes to the constitution," demonstrators chanted.
Banners read "The constitution is a guarantee for better future" and "Freedom and justice will be achieved by this constitution".
The rally came as the last of those who died in the stampede on Baghdad's al-Aima bridge during a religious ceremony were buried.
The stampede was sparked by rumours of that a suicide attacker was about to strike.
A gun battle broke out in Baghdad on Thursday as Shias marched on the bridge to blame al-Qaeda for the tragedy.
As they approached, Iraqi soldiers guarding the bridge fired in the air.
Believing they were under attack, Sunnis on the other side of the river opened fire. The girl was killed in the ensuing exchange of fire.
A number of people were also injured in the gun battle in northern Baghdad.
The incident was over quickly, but it has provided another reminder of the sectarian tensions which Iraq's leaders are so anxious to contain, the BBC's Jon Brain in Baghdad says.
In other developments on Friday:
- One person dies and at least four others are injured in a drive-by shooting outside two Sunni mosques in Basra, southern Iraq
- Two separate blasts - targeting a US convoy and a private security convoy - rock central Baghdad, injuring one person
- The US military announces that two of its soldiers were killed while on patrol in Baghdad on Thursday, and one soldier died south of the capital on Wednesday