Authorities said nearly all the 35 bodies found dumped around Baghdad and the southern city of Kut showed signs of torture.
Meanwhile the remains of 80 people, believed to be Kurdish victims of Saddam Hussein's regime, were unearthed in two mass graves near the northern Iraqi city of Kirkuk.
33 bodies found dumped
In Baghdad, 19 bodies were found during the morning in five neighbourhoods in the south and the west of the capital, while another 14 were found in the space of one hour in eastern and northern areas.
The bodies, all of men, were blindfolded and their feet and hands were tied, police said.
In Kut, 160 km south-east of Baghdad, police found another two bodies dumped on a highway. Both had been shot in the head and chest, said Maamoun Ajil al-Robaiei from the morgue at Kut hospital.
Bodies are frequently dumped on the streets of cities and in rivers across Iraq.
They usually show signs of torture, and the majority appear to have been killed by being shot.
Mass Kurdish graves found
A Kurdish security official said a total of 80 bodies were unearthed from two graves in Towb Zawa, 15 kilometres southwest of Kirkuk.
Tens of thousands of Kurds were killed in a military campaign in 1998 codenamed Anfal - Spoils of War - for which Saddam, his cousin Ali Hassan al-Majid, known as Chemical Ali, and five other former commanders are now on trial in Baghdad.
The security official said the 80 bodies were believed to date from Anfal, when the military razed villages, launched poison gas attacks and rounded up men, women and children before shooting them in mass graves in northern and southern Iraq.
"The remains of 18 bodies, mostly women and children, have been found in one of the graves. From their dress, they seem to be people who went missing during the Anfal campaign," he said.
Saddam and his six co-accused face charges of war crimes and crimes against humanity, but he and his cousin face the additional, graver charge of genocide, which also carries the death penalty.
They are likely to argue that their crackdown on the villages along the Iranian border was justified because Kurdish rebels and their leaders had committed treason by forming alliances with arch-enemy Iran.
Karbala attacks
A statement from the prime minister's office said Iraqi forces had received information that "terrorist elements" were planning attacks on Shiite pilgrims in Karbala.
Tens of thousands of Shi'ite pilgrims are expected in the city, 80 kilometres south of the capital, on September 9 to observe Shaaban, a mid-month religious celebration.
The troops surrounded the area of Jarf al-Sakhr, near Karbala, and "a group of terrorists opened fire on our forces, which prompted our men to respond", the statement said.
It said 14 gunmen were killed and another 22 were arrested. A total of 98 other suspects were briefly detained and later released "after it was proven that they were not involved in the terrorist operation," the statement said.
One soldier was also killed, and another was wounded, it added, while a large cache of weapons and ammunition was seized, alongside four vehicles "that the terrorists were planning to use in their criminal operations".
Troops killed
Meanwhile at least 10 US and two British troops have died in Iraq in a two-day period, most of them killed in rebel attacks.
The latest deaths brought the US military's losses in Iraq since the March 2003 invasion to 2,651, according to an AFP count based on Pentagon figures.
The British military also said that two of its soldiers were killed in a roadside bomb attack near the main southern city of Basra on Monday, while a third was seriously wounded.
The latest British casualties brought the military's losses in Iraq since the invasion to 117, a military spokesman said.
Iraq near handover
In other developments, the United States and Iraq hope to sign an agreement by next week to hand operational command of Iraq's new army to Prime Minister Nuri al-Maliki, Iraq said, after wrangles on wording had held up the accord.
A day after the government hailed the arrest of al-Qaeda in Iraq's purported deputy head as a coup against insurgents, the bodies of 33 men, some with their hands bound and bearing signs of torture, were found in Baghdad, and foreign forces announced the death of four Americans and two British soldiers.
In addition, a player for one of Iraq's biggest soccer clubs was kidnapped by gunmen in Baghdad just days before he was due to sign a transfer to a Syrian club, an Iraqi official said.
Transferring security from US forces to the Iraqi army it is training is key to Washington's plans to withdraw its 140,000 troops.
A handover ceremony set for Saturday was delayed over disagreements between Baghdad and Washington over the wording of a document outlining their armies' new relationship.
Denying there had ever been serious disagreement, government spokesman Ali al-Dabbagh said: "Both sides have agreed on the main issues. I think the document is ready to be signed, probably by the end of this week or early next week."
He said all remaining disagreements were "technicalities".