Two marines died when the aircraft crashed near the restive Sunni Arab town of Ramadi on Wednesday morning.
However the statement on an Islamist website could not be verified.
US Army General Rick Lynch said Thursday that the AH-1 Super Cobra, which had been flying low in support of ground troops, might have been shot down.
"People on the ground believe they saw a munition fired at the helicopter," he said. They "saw the helicopter break into pieces in midair and then crash."
US forces then "found in that general area ... a command and control bunker for enemy insurgents," Lynch said. An F-18 fighter jet was called in to bomb the bunker.
A US military policeman was killed Thursday near the town of Baquba, north of Baghdad, the military said, bringing to eight the number of servicemen killed over the past three days.
Al-Qaeda in Iraq is headed by Jordanian-born Abu Musab al-Zarqawi and is blamed for some of the deadliest attacks in Iraq.
Moroccan’s killed
In a separate statement, the group said it had decided to kill two Moroccan embassy staffers it is holding hostage as relatives pleaded for their release.
Al-Qaeda said the Moroccans were "loyalists of the oppressors and elements of the apostate regime in Morocco."
Embassy driver Abdelrahim Boualam and agent Abdelkrim El Mouhafidi went missing on October 20 while travelling on the treacherous highway between Amman and the Iraqi capital.
Morocco condemned the reported plan to kill the men as "extreme barbarity" and against the principles of Islam.
The government was "appalled" by this decision, saying it was "totally against the noble precepts of Islam" and the "fundamental values of humanity", the foreign and cooperation affairs ministry.
The ministry said it had sent a delegation to Amman to try and liberate the hostages but despite numerous pleas for their release the Al-Qaeda group had chosen to resort to "extreme barbarity.
Mouhafidi's wife, Liqa, and Boualam's brother, Mustapha, appealed Thursday for their freedom in remarks on Arabic satellite channels.
Call to unite
Meanwhile, Sheikh Hazem al-Araji, who is close to radical Shiite cleric Moqtada al-Sadr, called on Iraqis to "unite to fight terrorism and to get rid of people like Al-Qaeda."
In a sermon to worshippers at Baghdad's Al-Kazimiyah mosque, he said the extremists "say they are killing in the name of Islam, when they are apostates."
These groups "sometimes act in the name of Ansar as-Sunna (partisans of the Sunnis), but they are enemies of the Sunnis.
"You who call yourselves Qaeda al-Jihad (base of the holy war), you are the base of apostasy," he said, referring to Zarqawi's group.
Araji spoke during prayers at the beginning of Eid al-Fitr, the feast that marks the end of Ramadan, Islam's month of dawn-to-dusk fasting.
While Sunnis began the three-day holiday on Thursday, Grand Ayatollah Ali Sistani, the premier Shiite religious authority in Iraq, decreed celebrations in his community are to begin Friday.
But Sadr supporters ignored Sistani. In Sadr City, an impoverished Baghdad neighborhood where Sadr enjoys strong support, clerics called for celebrations to begin on Thursday.