"We call on the American forces to leave Iraqi cities, especially the unstable ones, to allow for their residents to exercise their electoral rights in a normal fashion," the Iraqi Concord Front (ICF) said on Thursday.
The ICF said continuing military operations in these areas, mostly north and west of Baghdad, were a "deliberate marginalisation of those who did not participate in past elections.
"As the election approaches, an escalation can be seen in military operations in those provinces that reject the occupation," it said.
That was a particular reference to al-Anbar, west of the capital, which is a key area of rebel activity.
Boycott a mistake
The fight against the US presence in the country is largely made up of Sunni Arabs, so the most unstable towns and cities are those where Sunnis have a strong presence among the populace.
Most Sunnis boycotted the January elections for an interim parliament, a move that many now acknowledge was a mistake since it largely sidelined them from politics over the past year.
Sunnis protested at the time that the polls were taking place under foreign occupation and that their community faced marginalisation by the majority Shia.
The Iraqi Concord Front is made up of the three main Sunni parties: the Conference for the People of Iraq, the Iraqi Islamic Party and the Iraqi National Dialogue.