The IIP said it would suspend all communication with US personnel until it got "a convincing explanation of what happened, accompanied by an official apology".
It also demanded assurance those responsible would be punished, compensation for the victims and the release of the five detainees.
Supporters of the IIP demonstrated against the raid on Saturday.
The incident has inflamed tensions in Anbar province, where Fullajah is located, ahead of provincial elections scheduled for the end of January.
Following the US invasion of Iraq, Anbar province had been the scene of major battles between US forces and Sunni fighters until 2006, when Sunni tribal leaders agreed to join forces with the US against al-Qaeda in Iraq.
|Al-Hashemi's party has been locked in a dispute with the Awakening Councils [EPA]
The move established the so-called Awakening Councils, which later spread to other Sunni areas.
The councils are seen as a successful US move in Iraq and have been one of the main reasons for recent security gains.
But the IIP has been locked in a bitter rivalry with the Sunni tribal leaders who joined forces with the US and that has raised concerns that the political tensions could spark violence and disrupt the Awakening Councils.
American forces handed over security responsibility for the province to the Iraqis on September 1, but they retain a presence in Anbar, which stretches west from Baghdad to the borders with Syria, Jordan and Saudi Arabia.