Insurgents launched yet another deadly blitz across Baghdad on Sunday, killing at least 40 people in an attack on a business school and setting off a minibus bomb near the Iranian embassy.

A suicide bomber triggered his explosive vest outside the School of Economy and Administration in east Baghdad, where the students are mainly Shiites, the blast ripping through a crowd of young men and women.

Terrified parents converged on the scene searching for their loved ones, some collapsing in horror at the sight of blood and human flesh sprayed across the front wall of the building.

"They sold us out!" one man cried out, reflecting a growing sentiment that an 11-day-old US and Iraqi security plan has failed to protect the city from those determined to foment sectarian war.

A security official said that at least 40 people were killed, and medics at the Imam Ali hospital said they were battling to save more than 30 seriously wounded people, many of them female students.

The school is an off-campus annex of Mustansiriyah University, which was also targeted by Sunni extremists on January 16 when a twin bomb attack killed at least 70 people and wounded around 140.

In another attack on Sunday, Iranian officials said their compound had not been deliberately targeted after a minibus exploded nearby amid mounting tension over Iran's relations with its war-torn neighbour.

The blast came at 8:45 am (0545 GMT) during the morning rush hour when roads were packed with people heading for work, many in nearby Iraqi ministries.

Tehran's embassy was not damaged, but amid the wreckage could be seen at least four unexploded artillery shells rigged to the bomb. Had they also detonated, the devastation would have been widespread.

"The police told us that it was a Kia minibus, and that two people were killed. It was close to the embassy, but we weren't the target," Iranian diplomat Khalil Saadati told AFP.

An Iraqi defence ministry official confirmed that two civilians died in the blast and eight more were wounded.

The blast ripped the bus apart, leaving only its shattered engine block amid scorch marks and a spray of deadly shrapnel. US Blackhawk choppers clattered overhead as a cloud of dust drifted over the embassy.

Later, a car bomb wounded five shoppers in the busy Karrada district, officials said.

Car bombs explode in Baghdad every day, as insurgent groups target the US-backed government and rival Sunni and Shiite factions fight a bloody sectarian turf war.

Death squad murders are down this month, however, since the launch of a city-wide crackdown by up to 90,000 US and Iraqi police and troops, but bombing continues and fighting has intensified in the outskirts.

Overnight, US artillery responded to insurgent mortar fire in the rural southern suburb of Boaitha, rocking Baghdad with thundering blasts.

On Saturday, a suicide bomber had attacked the home of Abdel Aziz al-Hakim, leader of the Supreme Council for the Islamic Revolution in Iraq, a party founded by exiles in Tehran and which retains close ties to Iran.

Washington accuses Iran of smuggling sophisticated weapons to Iraqi Shiite parties -- in December US forces arrested an alleged Iranian special forces officer in Hakim's compound -- and of funding sectarian militias.

On Friday, US forces arrested Hakim's son Ammar al-Hakim as he crossed the border from Iran. He was released the same day, but his detention triggered massive protests in Shiite cities.

Earlier this month, Iran's role in Iraq was highlighted when US commanders and senior Iraqi officials claimed that radical Shiite cleric Moqtada al-Sadr had decamped across the border.

Sadr's supporters deny this, but he has not been seen publicly for weeks amid persistent reports that senior cadres in his feared Mahdi Army militia have gone to ground to avoid the new US-Iraqi security plan.

The United States accuses Iran of fomenting trouble in Iraq, in particular by smuggling deadly armour-piercing roadside bombs called "explosively formed penetrators" to Shiite groups.

Police said on Sunday they found two bodies without heads or hands near a checkpoint close to Suleiman Beg, in northern Iraq near the city of Tikrit.

And two labourers were killed and one wounded by a roadside bomb in the disputed northern oil-rich city of Kirkuk.

In the "Sunni triangle" west of Baghdad, a suicide bomber late on Saturday detonated a fuel tanker outside a Sunni mosque in the town of Habbaniyah, where tribal chiefs have vowed to fight Al-Qaeda. At least 40 people were killed.