"We, the residents and the tribes, don't want al-Qaida in the city. We don't want to see the same violence we saw when the Americans were here," said Ayad al-Halbosi, a 22-year-old teacher in Fallujah.
Markets in the city began reopening Wednesday and some families returned to their homes, though residents complained of shortages of fuel and cooking gas. Civilian cars and trucks were seen on the road and traffic policemen were on the streets.
The militant gains in Anbar are posing the most serious challenge to the Shiite-led government since American forces withdrew in late 2011 after years of bitter warfare following the 2003 invasion that ousted Saddam Hussein's Sunni-led regime and propelled the formerly repressed Shiite majority to power.
The U.N. envoy to Iraq, Nickolay Mladenov, warned that the humanitarian situation in Anbar is likely to worsen as military operations continue.
Food and water supplies in Fallujah are beginning to run out, and more than 5,000 families have fled to neighboring provinces to escape the fighting, he said.
"The U.N. agencies are working to identify the needs of the population and prepare medical supplies, food and non-food items for distribution if safe passage can be ensured," Mladenov said in a statement.
The International Committee of the Red Cross also voiced concerns about the growing risks to Anbar residents, particularly in Fallujah. Patrick Youssef, head of the Red Cross delegation in Iraq, warned that ongoing power outages and dwindling medical supplies could leave health care facilities unable to provide proper care.
"We are ready to deliver more life-saving supplies and other humanitarian aid immediately to the areas hardest hit," Youssef said. "But we need to be given easier access and the necessary security guarantees."
Tensions have been simmering in Iraq since December 2012, when the Sunni community staged protests to denounce what they say is second-class treatment by al-Maliki's Shiite-led government.
Al-Qaida militants, emboldened by the civil war in neighboring Syria, have sought to position themselves as the Sunnis' champions against the government, though major Sunni tribes in Anbar and elsewhere oppose the group's extremist ideology and are fighting against it.
Schreck reported from Dubai, United Arab Emirates. Associated Press writer Sinan Salaheddin contributed reporting.
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