Between 12,000 and 15,000 Islamic State fighters remain in Iraq and Syria, a top US general said Wednesday, an indication of a significant dwindling of the jihadists' forces.

The US military only provides periodic updates on estimates of IS fighters but in 2015 and 2016, the Pentagon put the number at between 20,000 and 30,000 in the two countries.

Some months saw the jihadists being killed in the thousands, though initially at least they were able to replenish their ranks through a porous border with Turkey that now is effectively sealed.

Army Lieutenant General Stephen Townsend told reporters that among the many fighters killed in recent months are an "extraordinary number" of IS leaders, including many close to the group's elusive leader Abu Bakr al-Baghdadi.

"We have a specific campaign to hunt them and kill them," Townsend said in a video call from Baghdad.

"Almost all of Abu Bakr al-Baghdadi's inner circle has been killed in the last six months."

Still, he said about 2,000 IS fighters remain in and around western Mosul, defending the last portions of their former Iraqi bastion.

When the Mosul campaign began in October, officials estimated there to have been 3,000 to 5,000 IS fighters in and around the city.

Some of those fighters have fled west to the Tal Afar region and security forces have intercepted others who are trying to mingle with the civilian population "all over Iraq and Syria," Townsend said.

"We're focused on chasing them out in a sort of sequential campaign," he added.

A US-led coalition has since late summer 2014 been bombing IS in Iraq and Syria while at the same time supporting local forces doing the fighting on the ground.

Townsend cautioned against predicting when the defeat of IS might come.

"I don't expect (IS) to suddenly collapse from a lack of morale," he said.

"There's a portion that will break and run. The rest of them will fight as ordered or fight to the death."

source: AFP