The attack on the fighters, known as Sahwa, near a military base in the Madain area also wounded at least 56 people.
It was unclear how many of the victims were Sahwa fighters.
There was no immediate claim of responsibility for the attack, but suicide bombings are a tactic almost exclusively employed by Sunni extremists in Iraq, including the Islamic State (IS) group, which Sahwa militia forces have fought against.
In the northern city of Kirkuk, a gunman killed Colonel Dhargham Khairallah, the head of Kirkuk province's anti-terrorism forces, a police colonel and a doctor said.
The officer was being driven in Kirkuk's Al-Shorjah neighbourhood in a taxi to keep a low profile, but the gunman sprayed him with bullets from another car, according to the officer.
IS spearheaded a sweeping militant offensive that has overrun much of Iraq's Sunni Arab heartland since June – areas that Shiite-led government forces have sought local Sunni help to retake.
The Sahwa, or "Awakening" in Arabic, dates back to the height of the US-led war in Iraq, when Sunni tribesmen joined forces with the Americans to battle insurgents including IS's predecessor organisation, the Islamic State of Iraq.
The Sahwa were key to sharply but temporarily reducing violence, but when Iraq's government took over responsibility for their salaries they were sometimes paid late or not at all.
Now Sunni fighters, including the Sahwa and other armed tribesmen, again have an important role to play in the fight against IS.
The Iraqi government has distributed arms and ammunition to tribesmen, and Prime Minister Haider al-Abadi aims to establish a national guard made up of local fighters, though the necessary law has yet to pass parliament.
Iraqi security forces backed by US-led air strikes, Kurdish forces, Shiite militias and Sunni tribesmen have clawed back some ground from IS.
But major areas, especially north and west of Baghdad, remain outside government control.

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