About 13,000 Sunnis in the form of Popular Mobilization Forces are fighting against ISIL militants and are paid by the government, said Kazem al-Sayadi, a National Alliance MP.
The Sunni fighters and tribesmen have fought against the insurgents in Salahuddin province, north of Baghdad, he was quoted by the Arabic-language Al Sumaria news channel as saying.
On Tuesday, Iraq's Popular Mobilization Forces said they had taken charge of the campaign against ISIL terrorists to liberate the western province of Anbar.
Over 80,000 Iraqi volunteer forces will take part in a military operation to liberate the ISIL-held city of Ramadi, the capital of Anbar, a senior commander of the forces said.
Iraqi Premier Haider al-Abadi has vowed to recapture the city within days.
Iraq has been facing the growing threat of terrorism, mainly posed by the ISIL terrorist group.
The ISIL militants made swift advances in much of northern and western Iraq over the last summer, after capturing large swaths of northern Syria.
However, a combination of concentrated attacks by the Iraqi military and the volunteer forces, who rushed to take arms after top Iraqi cleric Ayatollah Ali al-Sistani issued a fatwa calling for fight against the militants, have blunted the edge of the ISIL offensive.