The US military must take decisive action to "destroy" Islamic extremists in both Iraq and Syria before the threat from the jihadists expands, a former American general said on Thursday.

Only the United States has the power and weaponry to lead a coalition -- including local Iraqi, Kurdish and tribal forces -- to confront the so-called Islamic State (IS), said retired four-star general John Allen, who led US troops in Iraq and served as the top commander in Afghanistan.

"The Islamic State is an entity beyond the pale of humanity and it must be eradicated. If we delay now, we will pay later," Allen wrote in a commentary in Defense One.

"IS must be destroyed and we must move quickly to pressure its entire 'nervous system,' break it up, and destroy its pieces," wrote the general, now a fellow at the Brookings Institution think tank.

Allen warned that the militants are well-funded, well-armed and displaying an alarming degree of battlefield acumen.

"IS is able to demonstrate substantial battlefield innovation and agility -- two qualities none of us can afford as IS continues its forward movement and attempts to consolidate," he wrote.

The former commander said the grisly execution of US reporter James Foley by the jihadists "brings home to us all what this group represents."

Allen praised President Barack Obama for his response so far, including limited air raids against the militants in northern Iraq, but argued that strikes against the jihadists should not be confined to Iraq but should apply to western Syria as well.

"We cannot leave IS a safe haven anywhere or a secure support platform from which to regroup or enjoy sanctuary across the now-irrelevant frontier between Syria and Iraq," he wrote.

With President Bashar al-Assad's regime waging a protracted civil war, Syria represented a "failed state," he said.

"Syria is a failed state neither capable of acting as a sovereign entity nor deserving the respect of one," he wrote.

Allen did not advocate deploying a large contingent of US ground troops and instead backed the use of American air power in support of allies such as Kurdish forces in northern Iraq.

"The tentative successes of the Kurds in rolling back IS from the Mosul Dam should offer a clear signal that this formula of employing indigenous forces coupled with American and allied firepower can be undertaken with effect," he said.

Allen also said Sunni tribes in Syria were ready to take on the extremists but were "begging" for more American and international help.