The 44 Sunni lawmakers also demanded the Iraqi troops pull out of cities in the province and that Ahmad al-Alwani, a Sunni lawmaker arrested Saturday, be released, China's Xinhua News Agency reported the bloc's spokesman, Dhafer al-Ani, said at a televised news conference.
The resignations came hours after hundreds of demonstrators battled with police and army forces in Ramadi, Fallujah and elsewhere in the province. A medical source at Ramadi's hospital told Xinhua at least 10 people were killed and about 40 others were wounded, and a provincial police source said at least two tanks and several military vehicles were burned.
The violence broke out in cities across Anbar province after police dismantled an anti-government protest site in Ramadi, police said.
The state-run Iraqia television channel said "local police, in cooperation with provincial authorities in Anbar, removed the tents from the protest site near Ramadi."
Tension in the province, a Sunni stronghold, has been high since Iraqi security forces captured al-Alwani and killed his brother, Xinhua said.
It added Sunnis have been protesting the Shiite-led Iraqi government, accusing it of marginalizing and indiscriminately arresting, torturing and killing Sunnis.
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