But the warrant triggered a political crisis, as the biggest bloc in parliament, al-Iraqiyya, accused Prime Minister Nouri Maliki of using the law to consolidate his grip on power.
He has fled to the Kurdish-controlled region of northern Iraq, and denies the accusations against him.
An arrest warrant was issued for Vice-President Tariq al-Hashemi, the country's most prominent Sunni Arab politician, on terrorism charges.
Wednesday's attack comes amid a marked deterioration in Iraq's fragile political process since the withdrawal of US forces from the country at the end of last year.
Awakening Council leaders have been the targets of many assassinations.
Mr Dwaiyeh was a member of the Awakening Councils, a group of Sunni fighters who fought alongside the US army against al-Qaeda-linked militants.
Mohammed Dwaiyeh's wife and a fourth son were also reportedly wounded when the gunmen burst into their home in Latifiya before dawn and opened fire.
A village elder and his three sons have been killed by gunmen south of the Iraqi capital, Baghdad, police say.
Wednesday, 18 January 2012 12:25
Gunmen kill Iraq village elder and three sons
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