An Iraqi newspaper said the helicopter crashed during heavy clashes in which Iraqi security elements attempted to arrest the imam of al-Masraf mosque.
On Friday, a US Army Blackhawk helicopter was shot down northeast of Baghdad, killing 12 US troops.
A Pentagon official said there was evidence in the wreckage that it may have been shot down by a surface-to-air missile.
US military officials in Baghdad have not confirmed what downed the helicopter and say an investigation into the crash is continuing.
In a statement which was obtained by Al Jazeera, the Islamic army in Iraq has said it was responsible for the attack on the helicopter.
US soldier killed
In Ramadi, ten civilians were injured in clashes between armed men and US troops. The US military said in a statement that US forces killed nine insurgents and wounded nine in three separate incidents in the town.
In Haditha, local residents found nine bodies while in Biji, five Iraqi soldiers were killed when an explosive device blew up.
The Iraqi police said a US military vehicle was destroyed and one soldier was killed when a US patrol was attacked by an explosive device in al-Tahrir district south of Baquba.
The US troops sealed off the site of the attack and searched the vicinity for the perpetrators, but none were found.
Seven British soldiers were wounded in Basra, five in a car crash and two in a rocket attack, said Katie Brown, a military spokeswoman.
The five injured in the car crash were in a SUV that was hit from the rear by a civilian car. The rocket attack targeted a British base at Basra Palace, the military spokeswoman said.
Also on Tuesday, a Shia professor and economist was shot dead by fighters in Baghdad's dangerous Azamiyah area, a predominantly Sunni neighbourhood.
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Diya al-Meqoter, who taught economics at al-Mustansiriya university, was shot several times in the head and chest during the attack.
Al-Meqoter was well-known for his work in helping poor people secure loans to start small businesses, police and his university dean said.
Mahdi al-Hafez, the former Iraqi planning minister, condemned the assassination, calling it "an ugly crime and a painful incident against an intellectual and well-known economist".