Meanwhile an Australian security contractor was among three foreigners killed in a small-arms attack on the road to Baghdad’s international airport.
Media reports said the attack occurred around midday on Wednesday.
Police announced the gruesome discovery of 57 bodies of men and children in Suwayrah, about 40 kilometres south of the capital.
They were believed to be Iraqi hostages, seized earlier this month.
“They were killed and they threw the bodies in the Tigris. We have the full names of those who were killed and of those criminals who committed these crimes,” President Jalal Talabani said.
The bodies were found in an insurgent stronghold downriver from Madain, where unconfirmed reports last weekend said Shi’ite hostages were taken by Sunni rebels, a report denied at the time by Iraqi officials.
“The terrorists committed crimes there, and it is not true that there were no hostages, there were,” the president said.
In a separate discovery, the bodies of 19 Iraqi soldiers, believed executed, were found in a football stadium in the town of Haditha, 260 kilometres northwest of Baghdad.
“These soldiers belonged to a group of 20 men who were travelling by bus to their base in Haditha when they were intercepted. They were taken to the stadium where they were executed,” an official said.
Elsewhere, insurgents continued their attacks against the government.
In Baghdad caretaker Prime Minister Iyad Allawi escaped an assassination attempt on Wednesday when a car bomb exploded near his convoy, killing at least two policemen.
“(Mr Allawi) had attended an important meeting to discuss the formation of the government and was on his way back home when a car bomber blew himself up near the convoy as it approached the checkpoint,” his spokesman, Thaer al-Naqib, said.
He said guards opened fire on the attacker as he drove towards the convoy.
“He did not stop and blew himself up almost near the middle of the convoy,” he said.
An interior ministry spokesman said that two policemen were killed and one wounded in the attack, which happened at about 11:00 pm (1900 GMT) and involved a truck packed with TNT and mortar rounds.
The ministry spokesman said a suspect identified as Amer Mijbel al-Medab, an officer in the previous army of Saddam Hussein, was arrested near the scene of the bombing.