Islamic State cannot be defeated without addressing “both sides of what is essentially at this point a nonexistent border” between Iraq and Syria, the chairman of the Joint Chiefs of Staff said Thursday.

The United States and its allies in the Middle East and beyond need to join together to defeat the terrorist group “over time,” Gen. Martin Dempsey said. Asked whether the United States would extend its current campaign of airstrikes in Iraq into Syria, Dempsey said airstrikes were “only one small part” of what is necessary to defeat the group.

“I’m not predicting those will occur in Syria, at least not by the United States of America,” he said. “But it requires the application of all the tools of national power–diplomatic, economic, information, military.”

President Obama has long resisted direct U.S. military intervention in Syria, where Islamic State is the strongest of several militant groups fighting both the Syrian government and U.S.-backed rebels. But the group’s rapid advance into Iraq, and this week’s videotaped execution of an American hostage it was holding in Syria, have led to calls to revisit that policy.

The Islamic State video said that photojournalist James Foley was beheaded in retaliation for U.S. strikes in Iraq. The air attacks continued Thursday as the U.S. Central Command announced an additional six strikes around Mosul Dam in northern Iraq.

Defense Secretary Chuck Hagel, at a Pentagon news conference with Dempsey, said that “we are looking at all options” to stop the expansion of an organization he said was as “sophisticated and well-funded as any group that we have seen.”

“They’re beyond just a terrorist group,” Hagel said. “They marry ideology, a sophistication of strategic and tactical military prowess. They are tremendously well-funded.”

Asked whether airstrikes against the group in Syria was under consideration, Hagel said that “we continue to explore all options…and how best we can assist partners in that area, the Middle East, particularly in Iraq.”

“We will continue to stay focused…on what we’re doing now and exploring all options as we go forward,” Hagel said.

At a Pentagon briefing Thursday, Secretary of Defense Chuck Hagel said the Islamic State is a "sophisticated" operation. (AP)

A senior Defense official, speaking on condition of anonymity following the news conference, said that no decision has been made to expand airstrikes into Syria, and the White House has not requested any new military options.

U.S. airstrikes in Iraq began on Aug. 8, as militants there continued their bloody sweep across the country and closed in on the Kurdish capital of Irbil, where the United States has military facilities and a consulate. U.S. military officials said Thursday that the U.S. military has carried out a total of 90 strikes, 57 of them in the vicinity of Mosul Dam. Earlier this week, Obama announced that Iraqi and Kurdish forces had retaken the dam, near Iraq’s northern border with Turkey, from Islamic State control.

Following the death of Foley this week, Obama called the Islamic State a “cancer” and Secretary of State John F. Kerry said the group must “be crushed.” Dempsey, who was more measured in his remarks Thursday, said it is possible for the United States to contain the group. But he said the threat of the Islamic State must be addressed in both Iraq and Syria.

“This is an organization that has an apocalyptic, end-of- days strategic vision and which will eventually have to be defeated,” Dempsey said. “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 one immediate concern about the deterioration in Iraq and Syria and the rise of the Islamic State is the number of Europeans and other foreigners who have traveled to the region to join the militant movement.

“Those folks can go home at some point,” Dempsey said. “It’s why I have conversations with my European colleagues about their southern flank of NATO, which I think is actually more threatened in the near term than we are. Nevertheless, because of open borders and immigration issues, it’s… an immediate threat.”

UPDATE: 9:02 p.m.: This piece has been updated to reflect additional reporting.