The incident came after the Iraqi security forces and allied Hashd Shaabi units fought fierce battles with Islamic State (IS) militants during the past years and reclaimed key cities and towns from the extremist group, including the provincial capital of Ramadi, some 110 km west of Baghdad.
Reuters news agency cited officials as saying that ten security personnel and one local official were killed in the strike.
Those killed were travelling in a convoy which had been deployed to support a dawn raid on suspected IS militants in the area.
According to a statement by the Iraqi Joint Operations Command their target, Islamic State militant Kareem Afat Ali al-Samarmad was arrested during the raid before the clashes took place.
Since 2014 the United States has been leading a military coalition against the Islamic State in Syria and Iraq, leaving thousands of civilian deaths and casualties.
Obaidi said an airstrike hit the gathering, killing the six police officers and wounding 20 others, including security officers, the mayor and town's police chief.
Col. Ryan Dillon, a US Army spokesman for the Combined Joint Task Force, said the incident is under investigation but US warplanes give support when requested and approved by the Iraqi military.More news: Patrol plane sights Kiribati ferry survivors
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It said it had requested "air support from the worldwide coalition".
As the special forces troops returned to base, they encountered a convoy of police and paramilitaries of the Hashd al-Shaabi [Popular Mobilisation Forces] that had been sent to support them.
In July 2017 Amnesty International said both Iraqi and coalition forces "failed to take adequate measures to protect civilians, instead subjecting them to a terrifying barrage of fire from weapons that should never be used in densely populated civilian areas".
"An inquiry has been opened", it added.
"We demand Iraqi government to investigate the attack and give an explanation on why such operation was conducted without informing local authorities", Obaidi said. US helicopters opened fire, according to a statement from Joint Operations Command, which coordinates Iraqi forces and the coalition. "We were asked for support and we provided it", Dillon told AFP.
Qais al-Khazaali, the head of the Iran-backed Asaib Ahl al-Haq militias, also blasted the airstrike.