The PUK, one of two main Kurdish political parties in Iraq's autonomous Kurdistan region, is led by Jalal Talabani, the Iraqi president and a key supporter of US efforts in Iraq.
Mosul lies close to the Kurdistan region. Kurdish militiamen have a presence in parts of the city.
Kabir Goran, deputy head of the PUK, said the air strike occurred around midnight on Thursday when a US helicopter attacked what he called a Kurdish peshmerga watchtower in eastern Mosul.
"We think they may have hit us by mistake," he said.
The US military statement said that during the operation, US forces identified armed men from a bunker near the targeted al-Qaeda building.
Calls were made in Arabic and Kurdish for the men to put down their weapons.
As air support was called in, the statement said small arms fire came from the bunker.
Also on Friday, police said armed men dressed in Iraqi army uniforms swept into a village south of Baghdad, kidnapping 13 civilians and killing at least 11 of them.
The attack occurred around 5am local time in Imam, a predominantly Shia village about 75km south of the Iraqi capital.
Police later found 11 bodies with bullet wounds to the head and chest, and they were believed to be those who had been kidnapped, police and the Iraqi army said.
First Lieutenant Murad al-Maamouri, an Iraqi army spokesman, acknowledged the assailants wore Iraqi army uniforms and drove military vehicles, but said they were not government soldiers.
Another US air strike late on Thursday killed eight suspected anti-government fighters and destroyed a building in Arab Jabour, a mostly Sunni Muslim suburb south of Baghdad, the US military said.
Separately, the US military said three US soldiers died on Thursday in fighting in western Anbar province, bringing the total number of US military deaths in Iraq this month to 33.
In another incident, a British soldier has been killed and three others have been injured in a roadside bomb attack in southern Iraq, the British ministry of defence said on Friday.
"We can confirm that there has been a roadside bomb attack on a Multi-National Force patrol southeast of Basra city which has resulted in the death of one MNF soldier", who is British, an MoD spokeswoman said.
"Three other soldiers have also been injured, one of whom is described as critical."