Updated

Top U.S. military brass and former administration officials are publicly pressuring the White House to consider taking the fight against the Islamic State into Syria, warning that the terror organization poses an unprecedented threat to the United States.

"ISIL is as sophisticated and well-funded as any group that we have seen. They're beyond just a terrorist group," Defense Secretary Chuck Hagel said Thursday, adding that the U.S. will have to take a "cold, steely hard look" and "get ready."

Hagel and Joint Chiefs of Staff Chairman Gen. Martin Dempsey spoke in ominous terms as they addressed the growing danger posed by the organization that aims to form a caliphate across northern Iraq and Syria, and possibly beyond.

Their comments suggested something more than a "limited" military mission -- as the White House says is being pursued in Iraq -- is ultimately needed to blunt, and defeat, the Islamic State.

Dempsey, speaking after IS militants beheaded American journalist James Foley, tackled the sensitive topic of whether the organization can be dealt with without uprooting their foothold in Syria.

"To your question, can they be defeated without addressing that part of their organization 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 nonexistent border," Dempsey said.

On Friday, Pentagon spokesman Rear Adm. John Kirby would not elaborate when asked whether a broader campaign was under consideration. He stressed that Dempsey and Hagel were referring to the need for a "regional approach," and said both the Pentagon and president understand this won't be over in a "matter of weeks."

Military analysts, though, say the comments Thursday are a clear sign that Pentagon leaders are pressing President Obama to approve an expanded campaign, potentially in Syria.

Whether such options might include airstrikes in Syria, or lesser measures, is unclear. Dempsey said airstrikes are not necessarily required, but Hagel said "we're looking at all options."

Dempsey pointed to the need for a "coalition in the region" to take on the terror group.

But retired Gen. Jack Keane, former Army vice chief of staff and Fox News military analyst, said "the air power campaign must be applied in Syria ... as well as in Iraq."

Keane said it's "pretty obvious" that Dempsey and Hagel are pushing the White House and said they are likely putting new military options before the president.

Former high-level military and diplomatic officials are applying similar pressure from outside Washington.

Retired Gen. John Allen, who led the International Security Assistance Force in Afghanistan, penned a column on Defense One saying the Islamic State "must be eradicated." He wrote that the U.S. and its allies should operate against the organization "from Mosul in the east across its entire depth to western Syria." As for the question of sovereignty in Bashar al-Assad's Syria, Allen called Syria a "failed state" not deserving the respect of a sovereign entity.

Former U.S. ambassador to Syria Robert Ford also said on NPR that there "absolutely" is a case for considering U.S. airstrikes in Syria. Speaking on Fox News on Friday, Ford echoed the comments, while saying "airstrikes alone do not solve the problem."

Airstrikes, though, raise the question of whether the U.S. would partner with Assad, the dictator whose ouster the White House previously sought amid the regime's bloody civil war with opposition groups, including IS.

Ford said Assad cannot be a "reliable partner," blaming Assad for boosting the Islamic State and its predecessor in Iraq in years past -- and questioning whether the regime is doing enough now to stop its advance.

Keane predicted that if the U.S. launches attacks against the Islamic State in Syria, "I don't think [Assad] will engage us."

Keane called for simultaneously boosting military support and funding to moderate opposition groups in Syria. But he said the incremental increases in airstrikes and advisers in northern Iraq do not constitute a military strategy.

Retired Maj. Gen. Bob Scales, a Fox News military analyst, said Congress is going to ultimately have to get involved if this becomes a broader military effort.

"What the military is trying to do is get ahead of it," he said. "I think Dempsey understands very clearly this is a multiyear campaign that is going to have to eventually involve Congress, the administration and the American people. He's trying to set the conditions and tell the American people, get ready. This is all starting over again."

The Associated Press contributed to this report.