Sheikh Rafie al-Fahdawi said the small town of Husseiba fell overnight when police and tribal fighters withdrew after running out of ammunition.
"We have not received any assistance form the government. Our men fought to the last bullet and several of them were killed," he told The Associated Press in a telephone interview.
Husseiba is about 7 kilometers (4 miles) east of Ramadi, where IS militants routed Iraqi forces last weekend in their most significant advance in nearly a year.
Al-Fahdawi said that with the fall of Husseiba, the militants have come closer to the strategic Habbaniyah military base, which is still held by government forces.
"The situation is very critical. The militants are about 5 kilometers from Habbaniyah base, which is now in great danger," he said.
A day earlier, IS militants captured the Iraqi side of a key border crossing with Syria after Iraqi government forces pulled out. The fall of the al-Walid crossing, also in Anbar, will help the militants to shuttle weaponry and reinforcements more easily across the Iraqi-Syrian border.
The Iraqi government plans to launch a counteroffensive in Anbar involving Iranian-backed Shiite militias, which have played a key role in rolling back the IS group elsewhere in the country. The presence of the militias could however fuel sectarian tensions in the Sunni province, where anger at the Shiite-led government runs deep.
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