Islamic State militants are the most dangerous threat the US has faced in recent years, Washington has warned.
Defence Secretary Chuck Hagel said US air strikes had helped to break the Islamist advance in Iraq, but the militants could be expected to regroup.
America’s top general Martin Dempsey stressed that IS could not be defeated without attacking their base in Syria.
The warnings come after IS posted a video showing the beheading of US journalist James Foley.
The US has now begun a formal criminal investigation into Mr Foley’s death, with US Attorney General Eric Holder warning that the country has a “long memory”.
It has emerged that a special US military mission tried but failed earlier this summer to rescue Mr Foley and other US hostages held in Syria.
The militants had also reportedly wanted a $132m (£80m) ransom for his release.
‘Apocalyptic vision’
Speaking at a news conference on Thursday, Mr Hagel described IS as an imminent threat.
“They are beyond just a terrorist group. They marry ideology, a sophistication of strategic and tactical military prowess, they are tremendously well-funded… this is beyond anything that we have seen.”
Meanwhile, Gen Dempsey, the chairman of the US Joint Chiefs of Staff, said IS was “an organisation that has an apocalyptic, end-of-days strategic vision and which will eventually have to be defeated”.
“To your question, can they be defeated without addressing that part of their organisation which resides in Syria? The answer is no. That will have to be addressed on both sides of what is essentially at this point a non-existent border.”
Neither Mr Hagel nor Gen Dempsey announced a change in the limited military campaign adopted by Barack Obama, and the US president is unlikely to deepen his involvement in Iraq or Syria, the BBC’s Barbara Plett Usher in Washington reports.
But US officials did not rule out additional action against IS in Iraq or Syria, our correspondent adds.
Hunt for killer
In the UK, police and security services are trying to identify the jihadist who appeared in footage of Mr Foley’s killing.
Unconfirmed reports suggest the man – who had an English accent – is from London or south-east England.
In the video of Mr Foley’s murder, IS militants threatened to kill another American if the US did not stop its air strikes against the group in northern Iraq.
US air strikes have continued near Mosul despite the warning.
On Wednesday, President Obama vowed to bring the perpetrators to justice.
“We will be vigilant and we will be relentless,” he said. “When people harm Americans, anywhere, we do what’s necessary to see that justice is done.”
Air strikes intensify
The US has been conducting air strikes across Iraq since 8 August, as part of a campaign against IS targets.
US aircraft destroyed or damaged four IS vehicles and several bomb placements in strikes near the strategic Mosul Dam in northern Iraq on Thursday, the military said.
There have been a total of 90 air strikes across Iraq since operations began, the Pentagon said.
Of those 90 strikes, 57 have been near the dam.
The US said Iraqi troops and Kurdish peshmerga fighters recaptured the dam with American assistance on Monday.
IS fighters have waged a violent campaign in Iraq and Syria, seizing large swathes of both countries.
The violence has displaced an estimated 1.2 million people in Iraq alone.
BBC News
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