The mourning process took place on Thursday as criticism mounts against the Shia-led government for failing to prevent the tragedy.
The tragedy highlighted the risks of assembling such large crowds of people in one of the world's most dangerous and unstable countries.
"This is a result of the inadequate performance of the interior and defence ministers which has caused such a loss of life," said Baha al-Aaraji, a Shia lawmaker affiliated to cleric Muqtada al-Sadr.
"They should be made to stand in front of the National Assembly and be questioned. If it is proven that they have failed to fulfill their responsibilities, they should be dismissed and stand trial," he said.
However, Shia political parties encourage huge turnouts at religious festivals to display the majority sect's power in the new Iraq.
But the huge crowds overtax the ability of police and security services to protect them.
Iraqi President Jalal Talabani, a Kurd, told state-run Iraqiya television that "the government should take measures for an honest investigation to determine how failures doubled the casualties."
Al-Jafari said neighbouring
countries had offered help
Prime Minister Ibrahim al-Jafari and the ministers of defence and health visited a hospital where many of the victims were taken.
The prime minister, a Shia, said neighbouring countries including Jordan and Iran had offered to help treat the victims.
"We are ready to send abroad any patient who needs medical treatment there," he said.
The government has proclaimed a three-day period of mourning after the disaster, which appeared to have been sparked by a rumour that a bomber was among the more than one million people gathering at a Shia shrine in the capital.
A day after the disaster, hundreds of people were searching for their dead relatives at Baghdad hospitals.
Many of the bodies were strewn on the floor outside the hospital's morgue, which itself was packed with corpses.
Dozens of bodies were identified and taken away for burial by their relatives, medical workers said.
Iraq's Ministry of Interior announced on Thursday that a total of 953 people had died and 815 were injured in the chaos the day before on a bridge in north Baghdad.
Panic caused the stampede
resulting in the deaths
But Health Ministry spokesman Qassim Yahya said 843 died and 439 were injured.
It was not possible to explain the difference.
Iraqi ministries routinely announce different death counts after disasters or major attacks, and discrepancies are often never reconciled.