The incident happened on a river bridge as about a million Shias marched to a shrine for a religious festival.
Witnesses said panic spread over rumours of suicide bombers.
Radical Sunni groups have often targeted Shias in the past, but Iraqi officials said the tragedy had nothing to do with sectarian tension.
Many victims, mostly women, children or elderly, were crushed or drowned.
Witnesses describe horror
So far, there have been at least 695 confirmed deaths.
Earlier, mortar rounds had been fired into the crowd, killing at least seven people.
About 36 others were injured when four mortar rounds landed close to the Kadhimiya mosque.
A Sunni group said it carried out the mortar attacks, according to a statement posted on a website frequently used by groups linked to al-Qaeda.
"The mujahedeen of the Jaysh al-Taifa al-Mansoura (Army of the Victorious
Sect) fired mortars and Katyusha rockets at the bastion of the infidels and
apostates ... to punish the genocides committed against Sunnis," it said.
Iraqis are preparing to vote on a proposed constitution for their country,
with Shia and Sunnis sharply divided on its contents.
Wednesday is the last day the majority of Iraqis can register to vote in October's referendum.
Panic
Iraqi Defence Minister Saadun al-Dulaim said that the only people
to die at the hands of insurgents were the seven killed in the mortar attack.
"What happened has nothing at all to do with any sectarian tension," he said live on Iraqi TV.
"People swarmed the bridge. There had to be a search operation at the end of the bridge, so crowds gathered and a certain scream caused chaos in the crowds and the crowds just reacted and this sorrowful incident took place."
Officials had earlier suggested that someone in the crowd deliberately triggered the stampede by saying they had seen a suicide bomber.
Television pictures showed large crowds of Shia pilgrims heading towards the Kadhimiya mosque to mark the martyrdom of the 8th Century religious figure Imam Musa al-Kadhim.
During the crush, iron railings on the Aima bridge leading to the shrine gave way and hundreds of people fell into the water.
The bridge links the staunchly Sunni area of Adhamiya on the east bank of the Tigris and the Shia area of Kadhimiya on the west bank.
Mourning
Thousands rushed to the banks of the River Tigris to search for survivors.
Young men stripped off their shirts and waded into the muddy water to retrieve
bodies floating downstream.
The incident has caused the single biggest loss of Iraqi life since the US-led invasion in 2003.
As the number of dead and injured continued to rise, Baghdad's hospitals struggled to cope, with many bodies and injured people left lying in corridors and on pavements outside.
The Iraqi government has declared three days of mourning.
