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- Iraqis on life during US invasion
He is believed to have been the group’s “war minister” since two of its other senior leaders were killed last year.
Abu Suleiman was shot dead in the town of Hit, west of Baghdad, say officials.
“Based on intelligence, Iraqi security forces carried out the raid that killed him,” Maj Gen Qassim al-Moussawi told Reuters.
He said US troops had not been involved in the operation.
Jassim al-Halbousi, the chairman of Anwar provincial council, said security forces tracked down Abu Suleiman while investigating an earlier suicide attack in nearby Ramadi which killed 11 people.
As the troops approached, he fled in a car laden with explosives, which blew up as they opened fire, the Associated Press quoted Mr Halbousi as saying.
ISI is a militant umbrella group that includes al-Qaeda in Iraq, responsible for suicide and bomb attacks across the country.
News of the death came as large-scale protests were held across Iraq demanding government reform and action against corruption.
At least five people were killed as some of the protests turned violent.
Overall violence in Iraq has dropped sharply since the 2006-07 wave of sectarian bloodshed, but insurgent bombings are still common.