BAGHDAD (AP) — Iraq’s prime minister urged al-Qaida-linked fighters who have overrun two cities west of Baghdad to give up the battle, vowing Wednesday to press forward with a push to regain control of the mainly Sunni areas.

The United Nations, meanwhile, warned that the area in Anbar province is facing a “critical humanitarian situation” as food and water supplies are starting to run out.

Sectarian tensions have been rising in Iraq for months as minority Sunnis protested what they perceive as discrimination and random arrests by the Shiite-led government. But violence spiked after the Dec. 28 arrest of a Sunni lawmaker sought on terrorism charges and the government’s dismantling of a months-old anti-government Sunni protest camp in the Anbar provincial capital of Ramadi.

As clashes erupted, al-Qaida-linked gunmen assaulted Ramadi and nearby Fallujah, cities that were among the bloodiest battlefields for U.S. forces during the war. The militants overran police stations and military posts, freed prisoners and set up their own checkpoints.

The United States and Iran have offered materiel help for the Iraqi government but say they won’t send in troops.

Speaking in his weekly television address, Nouri al-Maliki hinted of a possible pardon for members of al-Qaida’s local branch known as the Islamic State of Iraq and the Levant who abandon the fight.

“The war that is being fought by the Iraqi security forces, tribes and all segments of Iraqi society against al-Qaida and its affiliates is a sacred war,” he said. “I call on those who were lured to be part of the terrorism machine led by al-Qaida to return to reason.”

In return, he promised that his government will “open a new page to settle their cases so that they won’t be fuel for the war that is led by al-Qaida.”

The militant gains in the Sunni-dominated province of 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.

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,” he said in a statement.

Those residents who remain in Fallujah, 65 kilometers (40 miles) west of Baghdad, appeared Wednesday to be trying to restore some semblance of normalcy, though the situation remained tense.

A call went out over mosque loudspeakers late Tuesday calling on fleeing families to come back and militants to leave the city. Markets reopened and some families returned to their homes. Civilian cars and trucks were seen driving through the city and traffic policemen were on the streets.

Tensions have been simmering in Iraq since December 2012, when the Sunni community staged protests to denounce what they say is second-class treatments 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.