"Some 186 bodies have been recovered and accounted for in hospitals so far," a security source said.
Television pictures showed hundreds of thousands of pilgrims marching to al-Kadhimiya mosque in Baghdad's al-Kadhimiya district on Wednesday to commemorate the death of the seventh imam, Musa al-Kadhim, a revered religious figure among the Shia.
The stampede occurred on a bridge near the mosque where pilgrims fearing a bomber among them, jumped off into the Tigris River.
"Dozens of pilgrims fell in the river Tigris as they panicked following rumours of the presence of two suicide bombers in the crowd, while they were crossing al-Aaimmah bridge near the mosque," the source said.
Iraq's Deputy Health Minister Jalil al-Shammari confirmed that hundreds had been killed.
Television reports said about one million pilgrims were streaming towards the shrine from many parts of Baghdad and from outlying provinces.
A million pilgrims were heading
for the shrine, some crawling
Earlier, four mortar rounds slammed into the crowd, police Major Falah al-Muhammadawi said.
At least seven were killed and 35 wounded, a medical officer at Baghdad's al-Kadhimiya hospital said.
He added that half of the wounded were women.
Six other people were wounded in a separate attack when attackers opened fire on Shia pilgrims in Baghdad's al-Adhamiya neighbourhood, an Interior Ministry source said. The latest round of violence comes a day after US air strikes on suspected al-Qaida hideouts in Iraq near the Syrian border killed at least 56 people.
Charter still open
Meanwhile, US ambassador Zalmay Khalilzad, said that changes to the draft constitution were still possible, raising the hopes of Iraq's disgruntled Sunni Arabs.
The statement comes as the Sunni Arabs, whose community is believed to form the backbone of the anti-US uprising, were seeking alliances to defeat the charter in a 15 October referendum.
Khalilzad hinted that the draft constitution presented to parliament on Sunday after weeks of tortuous negotiations, which failed to bring the Sunnis on board, was still an incomplete document.
"If Iraqis amongst themselves, in the assembly and of course from outside, decide to make some adjustments to the draft that was presented two or three days ago, it is entirely up to them," he told reporters.
"I believe that a final ... draft has not yet been - or the edits have not been - presented yet, so that is something that Iraqis will have to talk to each other and decide for themselves"
US ambassador to Iraq
"I believe that a final ... draft has not yet been - or the edits have not been - presented yet, so that is something that Iraqis will have to talk to each other and decide for themselves."
President Jalal Talabani announced on Sunday that the draft was ready to be put to the referendum in October for the Iraqi people to decide on its fate.
The Sunnis are now mobilising to strike alliances across the sectarian divide with any ethnic or religious groups opposed to the charter, in a bid to defeat it in the referendum.
Sunni leaders said they were opening talks with the movement of Shia cleric Muqtada al-Sadr.
Meanwhile, in rising sectarian tension, Sunni leader Adnan al-Dulaimi called for the resignation of Interior Minister Bayan Baker Solagh, accusing the Shia-dominated government's security forces of responsibility in the murder of 37 Sunnis whose bodies were found last week.
"I demanded the dismissal of the interior minister because the ministry has become very politicised," said al-Dulaimi after a meeting with Khalilzad.
On Thursday, Iraqi police found the bodies, each killed with a bullet to the head, dumped in a stream south of Baghdad.