U.S.-led air strikes against Islamic State in Iraq have killed three of the militant group's top leaders but not senior commander Abu Bakr al-Baghdadi, U.S. officials said on Thursday.

Among those killed was Abd al Basit, whom the officials described as the group's military 'emir,' and Haji Mutazz, a deputy to Baghdadi. Those strikes took place between Dec. 3 and Dec. 9, they said.

They also confirmed last month's killing of Radwan Taleb al-Hamdouni, whom local medical sources had described to Reuters at the time as the radical militant group's leader in the northern city of Mosul.

News of the killings, first reported by the Wall Street Journal, came the same day the top U.S. commander of coalition efforts against the Islamic State, Lieutenant General James Terry, hailed the impact of four months of air strikes in Iraq.

"We've made significant progress in halting that (militant) offensive," Terry told reporters.

He pointed to successful air strikes this week around Iraq's Sinjar Mountain and Zumar. Those strikes helped Kurdish peshmerga fighters fight their way to Sinjar mountain and, according to a Kurdish leader, free hundreds of people trapped there by Islamic State fighters.

At the same time, Terry outlined a long fight ahead, cautioning it would take several years to build necessary capabilities of Iraqi forces, who crumbled during the Islamic State's offensive this summer.