WASHINGTON (AFP) - The murder of American journalist James Foley by the so-called Islamic State (ISIS) is the extremist group's "first terrorist attack against the United States", a former head of the CIA warned Wednesday.

Mr Michael Morell, a former deputy director of the intelligence agency who was its acting chief between 2012 and 2013, said the jihadist group is trying to intimidate Washington into calling off air strikes.

"And I think our response should be and our response will be to not do that. In fact, we should pick up the pace here," he told CBS News, referring to recent US strikes against ISIS militants in Iraq.

"The definition of terrorism is political violence, violence for political effect. So we should mark this date down because this is ISIS' first terrorist attack against the United States."

The Islamic State, formerly known as the Islamic State in Iraq and the Levant (ISIL), declared itself a "caliphate" in late June and has since added a swath of northern Iraq to territory it holds in eastern Syria.

Earlier this month, US President Barack Obama ordered US warplanes to strike ISIS targets in Iraq to defend the Kurdish regional capital Erbil and civilian refugees fleeing the jihadist advance.

This week, with assistance from US bombing runs, Kurdish and Iraqi forces began to push ISIS forces back and recaptured the strategic Mosul dam.

On Tuesday the group released a video showing the execution-style murder of Mr Foley, a 40-year-old US reporter who was captured in Syria in late 2012 and held hostage ever since.

In addition to rallying extremist elements of the Sunni insurgencies against the governments of Iraq and Syria, ISIS has recruited radical jihadists from around the world, including Western countries.

Mr Foley's killer spoke with a British accent in the released footage, increasing fears that the group may one day mobilise foreign fighters to strike targets in Europe and America.