"Hundreds of people started running and some threw themselves off the bridge into the river," the source said.
"Many elderly died immediately ... but dozens drowned, many bodies are still in the river and boats are working on picking them up."
Most victims were women and children who "died by drowning or being trampled", an Interior Ministry official said.
"At 10:30 pm the confirmed death toll is 852 and it is still rising," said Dr Jaseb Latif Ali, a general manager at the Health Ministry, who said earlier the ministry expected the toll to top 1,000 people.
It was by far the biggest loss of life in such a crowd since more than 1,400 pilgrims died at Makkah during Haj in 1990.
In a country inured to mass bloodshed on its streets, there was profound shock and Prime Minister Ibrahim Jaafari declared three days of mourning. Constant coverage on national television included an appeal for relatives to claim a baby held up to the camera. He was found next to his mother's body.
Interior Minister Bayan Jabor and two other top Shia officials blamed Sunni insurgents for the stampede, saying one had spread a rumour there was a suicide bomber in the crowd.
But Defence Minister Saadoun al-Dulaimi, a Sunni Arab himself, said the stampede was not related to sectarian tensions gripping the country since the US-led invasion in March 2003.
"What happened has nothing at all to do with any sectarian tension," he said on television. Some witnesses blamed poor organisation for the death toll.
ATTACK, THREAT Whatever sparked the rush for safety, the fear that a bomber might be on the loose was well grounded after previous attacks on Shia religious events in the last two years.
Three separate mortar and rocket attacks on the crowd heading to the mosque to commemorate the martyrdom of Musa al-Kadhim had killed seven people before the stampede. They were claimed by a little known Sunni Muslim group.
Tensions are high among Iraq's rival religious and ethnic communities ahead of a referendum on a new constitution for the post-Saddam Hussein era.
Television images showed people clambering down from the bridge to escape the surging crowd and piles of slippers left behind by the crush of people.
Hysterical women knelt over corpses, wailing and praying.
Ambulances rushed to the scene and people hoisted bodies onto stretchers, while others lined the river bank and crowded the bridge.
Scores of bodies were covered with whatever was around - foil, clothes or plastic sheeting. A woman wept over the body of her dead child in al-Nu'man hospital. Dozens of bodies were strewn across the floor.
The hospital was filled with the sounds of screaming and wailing as disconsolate men and women searched for loved ones.
President Jalal Talabani said it was "a great tragedy which will leave a scar on our souls".
INSURGENCY UNABATED Despite the draft constitution, there has been no easing in an insurgency waged by Sunni Muslims, dominant under Saddam, and international guerrillas inspired by Osama bin Laden.
The US-led coalition invaded Iraq in March 2003 and has been battling insurgents, while Iraqis have tried to form a new post-Saddam constitution and government.
The persistent fighting has helped in pushing down President George W. Bush's approval rating to a career low of 45 percent, according to an ABC News/Washington Post poll.
The US war in Iraq now costs more per month than the average monthly cost of military operations in Vietnam in the 1960s and 1970s, according to a report issued on Wednesday.
The report entitled, "The Iraq Quagmire" from the Institute for Policy Studies and Foreign Policy in Focus, both liberal and anti-war organisations, put the cost of operations in Iraq at $5.6 billion per month. This breaks down to almost $186 million a day.
"By comparison, the average cost of US operations in Vietnam over the eight-year war was $5.1 billion per month, adjusting for inflation," it said.
CONDOLENCES Iran on Wednesday led international horror and outrage over the deaths of hundreds of people killed in a stampede as they headed to a Shia shrine in Iraq, blaming "suspicious hands" bent on causing havoc in the country.
Iranian Foreign Ministry Spokesman Hamid Reza Asefi, quoted by the student news agency ISNA, expressed his country's "condolences and sympathy with the Iraqi people and the government."
Asefi added, "Suspicious hands are involved in conspiracies to incite violence and bloodshed among different Iraqi groups and tribes so that they disturb the security and calm of the Iraqi people."
Syria also expressed its "sorrow and sadness" over the incident that "cost the lives of hundreds of people among the brotherly Iraqi people," a foreign ministry spokesman said.
"The Syrian government and people express their sympathy to Iraqis and to the families of the victims, and they wait for the day when security, stability and progress reign in the country," the unnamed official said, quoted by the state news agency Sana.
UN Secretary General Kofi Annan lamented the stampede and expressed his condolences to the families of the victims and to the Iraqi government.
"The Secretary General has learned with great sadness of the human tragedy that took place today in Baghdad," Annan's spokeswoman Marie Okabe told a press briefing. In Washington a State Department spokesman said the United States deeply regretted the tragic loss in human lives among the pilgrims. "Our sincere condolences and thoughts and prayers go out to the many Iraqi families who lost loved ones in this tragedy," Sean McCormack said.
Britain also condemned the attack and blamed 'terrorism' for inciting the deaths. "This is a most shocking and terrible tragedy, initiated by terrorism, and its scale almost defies imagination," Foreign Secretary Jack Straw said in a statement.
Arab League Secretary General Amr Mussa expressed his condolences and called for a "redoubling of Arab efforts to support the Iraqi people in their sad hour."
The Vatican's representative in Iraq Monsignor Fernando Filoni expressed the "solidarity and prayers of the Iraqi Catholic community" for the victims, saying it was truly tragic that a public religious demonstration had become a drama, according to the Vatican Asianews agency.
Italian Prime Minister Silvio Berlusconi, German President Horst Koehler, Greek Prime Minister Costas Karamanlis and Polish President Aleksander Kwasniewski also sent their condolences.