Negotiators are working on a deal to evade an Iraqi military intervention in the city of Fallujah, under which al-Qaeda-linked armed groups who seized the city would cede control to Sunni Muslim tribal leaders.
Military and local officials said on Friday that tanks, artillery and troops around the city, 70km west of Baghdad, would not attack while efforts to end the standoff peacefully were under way.
"The decision was made not to attack the city and to create space for local leaders to defuse the crisis," said Falih al-Essawi, a member of Anbar's provincial council who is involved in the negotiations with community leaders in Fallujah.
"The central government totally agreed to this and they fully backed us," Essawi told Reuters news agency.
Fighters of the al Qaeda-linked Islamic State of Iraq and the Levant (ISIL), which is also fighting in neighbouring Syria, took control of Fallujah and parts of nearby Ramadi on January 1, shortly after the Shia-led government ordered the dismantling of year-old vigils by Sunni tribesmen protesting its rule.
Although they are against central army's interference, Sunni pro-autonomy tribes have been battling al-Qaeda fighters alongside local security forces.
At least 60 civilians, gunmen and tribal fighters have been killed in the two cities since the trouble erupted, 43 of them in Ramadi and 17 in Fallujah, health officials in Anbar province said. They had no word on military casualties.
The clashes added to a series of challenges faced by Prime Minister Nouri al-Maliki amid growing discontent among Sunni provinces, including Anbar, who claim they are treated as second-class citizens.
The vast western desert region was previously the heart of the insurgency after the 2003 US invasion that toppled Saddam Hussein and brought about Shia majority rule.
A senior US official said Washington was encouraging the government to take a "patient, deliberate and restrained" approach to the Fallujah crisis. "I don't anticipate a move into the city by the armed forces," he told reporters on Thursday.
The UN Security Council condemned the ISIL attacks in Iraq and urged the Iraqi tribes, local leaders and security forces in Anbar province to expand and strengthen their cooperation to combat violence and terrorism.
"The Security Council recognises that Iraqi security forces, local police and tribes in Anbar province are showing great courage as they fight to defeat ISIL in their cities," the 15-member council said in a statement on Friday.