President Donald Trump tweeted about the incident, saying: "Five Most Wanted leaders of ISIS just captured!".
The second leader, Ismail al-Eithawi, who had been captured previously, was said to have been told to use his phone to summon the others. Those held include Saddam Jamal, a Syrian who served as the group's governor of Syria's eastern Euphrates region.
The Iraqis sent the Turks an intelligence file they had amassed on Ithawi, and the Turkish security forces arrested him Feb 15, and extradited him to Iraq, this official said. Jamal was shown on Iraqi state television on Wednesday night, wearing a yellow prison uniform.
Hashimi said the operation was carried out in cooperation with USA forces, part of an American-led coalition fighting against Islamic State on both sides of the Iraqi-Syrian border.
An Iraqi rapid response forces member walks past a wall painted with the flag commonly used by ISIS, in Mosul, January 8, 2017.
Incumbent Prime Minister Haider al-Abadi has cautiously trodden a diplomatic middle course between Tehran and Washington, ensuring the cooperation of both in the war against IS, which overran a third of Iraq in 2014. The Iraqi air force has carried out several air strikes since past year against Daesh positions in Syrian territory.
Islamic State, however, continues to carry out bombings, assassinations and ambushes, and remains active in neighbouring Syria where it has also lost most of its territory.