About 45,000 jihadists have been killed in Iraq and Syria since the US-led operation to defeat the Islamic State group began two years ago, a top general said Wednesday.

"We estimate that over the past 11 months, we've killed about 25,000 enemy fighters. When you add that to the 20,000 estimated killed (previously), that's 45,000 enemy (fighters) taken off the battlefield," said Lieutenant General Sean MacFarland, who commands the US-led coalition campaign against IS.

MacFarland said estimates for the overall remaining strength of IS vary from about 15,000 to 30,000 but he noted the jihadists are having increasing difficulties replenishing their ranks.

"The number of fighters on the front line has diminished. They've diminished not only in quantity but also in quality -- we don't see them operating nearly as effectively as they have in the past, which makes them even easier targets for us," MacFarland told Pentagon reporters via a videocall from Baghdad.

"As a result, their attrition has accelerated here of late," he added.

Officials also estimate IS has lost 25,000 square kilometers (9,650 square miles) of the territory it once held in its self-declared "caliphate" in Iraq and Syria, or about 50 percent and 20 percent respectively in each country.

The US-led military effort against the Islamic State group started exactly two years ago, aimed at halting the jihadists as they swept across Iraq and Syria.

MacFarland was upbeat about the eventual recapture of Mosul in Iraq and Raqa in Syria, saying it would herald the "beginning of the end" of the campaign.

But critics have blasted the pace of the war, which got off to a slow start and, despite more than 14,000 air strikes and an intense effort to train partner forces, still has not routed IS from much of its territory.

MacFarland, who has headed the US-led coalition for almost a year, said he had seen major progress.

"You don't hear the word 'stalemate' anymore. That's because over the past year with our partners, we were able to seize the initiative," MacFarland said.

"We now talk about maintaining the momentum of the campaign in both Iraq and Syria. In other words, we spend more time thinking about what we will do to the enemy than we spend thinking about what the enemy might do to us."

Experts do foresee the eventual collapse of IS, but the jihadists are fighting back by calling on followers to launch attacks across the globe and are likely to persist for years as a terrorist organization.