Obama made the comment in an interview with CNN on Friday, which will air in full on Monday.
Disregarding the root causes of the upheaval, which critics see as resulting from the U.S. invasion of Iraq, Obama told MSNBC that "forces that could keep the country together are weaker" now.
Speaking to CNN, Obama said that "part of the task now is to see whether Iraqi leaders are prepared to rise above sectarian motivations, come together, compromise. If they can't there's not going to be a military solution."
Without such unity, he said "there's no amount of American fire power that's going to be able to hold the country together."
Asked by CNN if if the U.S. could "protect its national interests" against the threat posed by ISIL without also going into Syria, Obama said that efforts like "taking targeted strikes where necessary" would be part of the U.S. counter-terrorism strategy regardless of the current situation in Iraq.