US and Iraqi troops have killed about 250 militants in fierce fighting around the holy city of Najaf, police say.
A pillar of smoke marked the spot where the US helicopter crashed
The battle raged all day as US-backed Iraqi army units fought the previously unidentified group in orchards on the northern outskirts of Najaf.
Three Iraqi soldiers had reportedly died in the battle and 21 were injured.
The US military said two of its troops died when their helicopter was shot down, but did not confirm any of the Iraqi casualty figures.
An Iraqi official in the Najaf governor's office told the BBC that 21 Iraqi soldiers had been injured in the clashes, which occurred in a neighbourhood called Zarqa, and the Iraqi army was sweeping the area.
Unnamed Iraqi sources said that the insurgents were from a previously unknown militant group calling themselves the Army of Heaven, or Soldiers of Heaven.
Asaad Abu Gilel, the governor of Najaf province, said that the gunmen had been intent on attacking Shia clerics and pilgrims marking the holy festival of Ashura.
"They are well-equipped and they even have anti-aircraft missiles. They are backed by some locals," he said.
Earlier on Sunday seven Iraqi children died after their schools were targeted - five in Baghdad where a mortar hit a high school and two in a bomb attack at a primary school in Ramadi
Pupils at the secondary school in the mainly Sunni Adil district in west Baghdad were taking a break from lessons when two mortars landed in the yard.
Five girls were killed and 20 other pupils injured as the blast blew out classroom windows, spraying the children with debris and shards of glass.
The school is in a Baghdad district hit by previous sectarian attacks
It was not clear who fired the mortars but the school is in a district which has been the scene of frequent reprisal attacks by Sunni and Shia extremists.
A primary school in Ramadi, north-west of Baghdad, was caught up in the violence when a suicide truck bomber attacked a nearby Iraqi security base.
In other violence on Sunday:
- A car bomb in the Sadr City district of Baghdad killed at least four people
- A bomb killed at least five people outside a warehouse in the mainly Kurdish Almas district of central Kirkuk
- Gunmen ambushed a senior official in Iraq's industry ministry as he drove to work, killing him, his daughter and two other people.
The wave of attacks comes as Iraqi and US forces are gearing up for a security crackdown in a bid to halt the sectarian violence that is claiming hundreds of lives in Iraq every week.
Earlier, Iraqi police said 54 unidentified bodies had been found in and around the capital on Sunday alone.
On Saturday, police said 40 bodies were found - such deaths are generally attributed to sectarian violence.
The UN says that, on average, just under 100 people die through violence each day in Iraq.
The latest violence comes as Shia Muslims mark Ashura, one of their holiest festivals.
Thousands of pilgrims from across Iraq and beyond descended on Karbala to take part in ceremonies marking the martyrdom of Imam Hussein, a grandson of the Prophet Mohammad, in 680.
In the past the festival has been hit by co-ordinated attacks, so some 10,000 Iraqi police and security forces were on duty in Karbala as part of a tightening of security.