Hagel said the U.S. airstrikes have helped Iraqi and Kurdish fighters regain their footing in Iraq. But the secretary also said in a question-and-answer session with reporters that the well-resourced Islamic State militants can be expected to regroup and stage a new offensive.
Dempsey said that taking on the Islamic State more forcefully would not necessarily require airstrikes by the U.S. in Syria, although Hagel appeared to leave open that possibility by saying, "We're looking at all options."
Hagel said operations the U.S. military has undertaken so far "have stalled ISIL's momentum and enabled Iraqi and Kurdish forces to regain their footing and take the initiative." ISIL and ISIS are alternate acronyms for the Islamic State group that is an outgrowth of the al-Qaida terrorist network.
The U.S. has restricted its military action to Iraq, but concerns have increased as the Islamic militant group extends its reach from safe havens in Syria across the Iraqi border.
Dempsey, who served multiple tours in Iraq during the 2003-2011 war, was pointed in his comments about what it would take to ultimately defeat the Islamic State group.
"They can be contained, not in perpetuity," Dempsey said. "This is an organization 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 organization which resides in Syria? The answer is no," he said. "That will have to be addressed on both sides of what is essentially at this point a nonexistent border.
"And that will come when we have a coalition in the region that takes on the task of defeating ISIS over time," Dempsey added, using another acronym for the group. "ISIS will only truly be defeated when it's rejected by the 20 million disenfranchised Sunni that happen to reside between Damascus and Baghdad."
Neither Hagel nor Dempsey gave any indication of an imminent change in the U.S. military approach in Iraq, which President Barack Obama has said will include further airstrikes but not the introduction of American ground forces.
The Pentagon on Thursday said U.S. warplanes had launched six airstrikes overnight to help solidify Iraqi and Kurdish forces' efforts to retake and maintain control of the Mosul Dam.
It said the latest strikes destroyed or damaged three Humvees, multiple roadside bombs and another insurgent vehicle. The attacks brought to 90 the number of U.S. airstrikes in northern Iraq since Aug. 8. Fifty-seven of the 90 have been in support of Iraqi forces near the Mosul Dam.