Reports from Iraq say armed groups have seized parts of the western cities of Fallujah and Ramadi.
Fighting erupted in Anbar Province on December 30 after security forces tore down a protest camp near Ramadi, inflaming simmering tensions between local Sunni Arabs and the Shi'ite-led government of Prime Minister Nuri al-Maliki.
Security forces have since withdrawn from some areas of Ramadi and Fallujah.
AFP news agency quoted an Interior Ministry official as saying on January 2 that half of Fallujah was in the hands of an Al-Qaeda-linked group, the Islamic State in Iraq and Levant.
The unidentified official said that in Ramadi, some areas were controlled by the group's fighters and other parts by tribesmen.
Reports said vehicles carrying armed men and black flags distinctive of Al-Qaeda were seen in the two cities.
Local officials said on January 1 the militants had seized weapons and freed some prisoners. Some police stations were reportedly set on fire as well.
Those attacks came only hours after the governor of Anbar Province lifted a curfew that had been in place since December 30, when fighting erupted in many parts of the mainly Sunni province.
Maliki had said civilian police could resume control of security in Anbar Province. However, the province's regional government has appealed to Maliki to keep the army in Anbar as a result of the fresh unrest.
Earlier last year, Sunnis launched mass demonstrations in several Iraqi provinces in which they form a majority, to denounce Maliki's Shi'ite-led government.
The protesters demanded the repeal of laws they claim target Sunnis, including one that prohibits former members of the Baath Party of ex-dictator Saddam Hussein from holding senior government positions.
Shi'ite Militia Commander Arrested
Elsewhere in Iraq, security forces arrested the leader of an Iranian-backed Shi'ite militia.
A spokesman for the Iraqi Interior Ministry said on January 2 that Wathiq al-Batat, the commander of the Al-Mukhtar Army, was arrested in Baghdad on January 1. It was not immediately clear on what charges he was arrested.
The Al-Mukhtar Army is a relatively new Shi'ite militia, which has said it is supported by Iran.
Batat claimed responsibility in November for firing six mortar shells near a border post in Saudi Arabia. There were no casualties, but Batat said the attack was a warning over the Sunni-ruled kingdom's stance toward Shi'a.
The fresh unrest comes as the United Nations Mission in Iraq announced that violence had claimed the lives of 7,818 civilians in 2013, the highest annual death toll in years.
The UN figures gave a total of 759 people killed in December alone, including 661 civilians and 98 members of the security forces.
Based on reporting by AFP, dpa, AP, and Reuters