Still, neither official suggested US military action there was imminent.
"We're just not there yet," said a senior US defense official, speaking on condition of the anonymity.
Republicans called on Sunday for more aggressive US action to defeat Islamic State militants in Syria and Iraq, accusing President Barack Obama of policies that have failed to thwart potential new threats on US soil.
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At the White House, spokesman Josh Earnest said Obama would consult Congress on whatever he decided on Syria, but would not necessarily seek congressional approval. He said Obama had not made any decisions on whether to use airstrikes against Islamic State militants in Syria.
Earnest said the Islamic State threat was a different situation from a year ago when Obama said he wanted Congress to approve the use of airstrikes to stop Syrian President Bashir al-Assad from using chemical weapons on his own people.
Obama sat down for talks on Monday with Defense Secretary Chuck Hagel.
Dempsey, Thomas said, believed that Islamic State needed to be pressured in Iraq and Syria and that defeating the group would require a sustained effort over an extended period of time "and much more than military action."
Although the US air campaign launched this month has caused some setbacks for Islamic State, they do not address the deeper problem of sectarian warfare that the group has fueled with its attacks on Shi'ites.