Washington is making preparations to withdraw the estimated 40,000 troops remaining in Iraq by the end of December.
A senior U.S. military official in Iraq told CNN on condition of anonymity that a combat brigade was returning to the United States early in part because of issues related to legal immunity.
Iraqi officials had said they opposed immunity after Prime Minister Nouri al-Maliki was given the authority to negotiate for a continued military presence to help train Iraq's armed forces.
Officials said a majority of the discussions with Iraq are over but Pentagon spokesman George Little was quoted as saying that talks regarding the final decision on the U.S. military role in Iraq "are ongoing."
A protester in the eastern Iraqi city of Khanaqin set himself on fire, but lived, to protest orders from Baghdad to remove the Kurdish flag from government institutions. Diliar Hassan, a Kurdish lawmaker on the Diyala provincial council, told the Voices of Iraq news agency about 20,000 people across the country turned out to protest the central government's decision.
Arabs, Kurds and ethnic minority groups sprinkled throughout Iraq's north are squabbling over access to oil, autonomy and the disputed territories, a swath of land stretching from Sinjar in the northwest to Khanaqin in the north of Diyala province.
Tensions between Kurdish and Iraqi forces nearly erupted into violence in Khanaqin in 2008.