In public comments Tuesday, Dempsey said the U.S. could provide weapons that might make the rebels more "militarily effective."
But, he warned, it's not clear "whether the military effect would produce the kind of outcome I think that not only members of Congress but all of us would desire, which is, you know, an end to the violence, some kind of political reconciliation among the parties and a stable Syria."
However, a U.S. official said military planners believe that it would be possible to vet the rebel fighting forces and that those under Free Syrian Army chief Gen. Salim Idriss and the Supreme Military Council are seen as independent of al-Nusra.
The official said the military planners also believe that Idriss' forces would be prime candidates to receive arms, if and when Obama makes the decision to start providing lethal assistance.
Arming the rebels could take any number of paths. If ordered, the U.S. military could provide the weapons to rebel groups, or the Pentagon could use the State Department as an intermediary and transfer the weapons through those channels. Under a more covert scenario, the CIA could secretly provide the arms.
At the Pentagon on Wednesday, press secretary George Little said there are discussions underway on how to bolster humanitarian assistance and how to engage even more closely with the opposition forces.
"We're fully cognizant of the role that extremist groups in Syria are playing," Little said. "We understand the dynamics that that creates."
He said the U.S. has to also look beyond any move to bring an end to the Assad regime, and work with allies on what a post-Assad Syria would look like.
Dempsey, however, also noted that during these difficult fiscal times, the U.S. military could do whatever was needed or ordered in Syria, but would likely require supplemental funding in order to sustain any operations over time. He said the military options are ready, although he has not yet been ordered to take any action.
Obama has said all military options are on the table, but there has been little appetite for putting U.S. military boots on the ground in Syria.
Associated Press writers Julie Pace and Matthew Lee in Washington, Edith M. Lederer at the United Nations and Zeina Karam in Beirut contributed to this report.
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