He said that Washington is concerned about a possible ouster of President Bashar al-Assad due to the rise of the Islamic State, which has already seized large areas of Iraq and Syria, forcing millions to flee the country.
"I think that's a legitimate concern, Brennan said, in reference to the White House's fears over who might succeed Assad in the future.
He singled out an array of "extremist elements", including the Islamic State militants and al-Qaeda veterans, who he said are "ascendant right now" in some parts of Syria.
"The last thing we want to do is allow them to march into Damascus. That's why it's important to bolster those forces within the Syrian opposition that are not extremists," Brennan said.
He stressed that "none of us, Russia, the United States, coalition, and regional states, wants to see a collapse of the government and political institutions in Damascus."
His remarks came as State Department spokeswoman Jen Psaki made a fresh call for President Al-Assad to stand down.
Psaki pointed out that without Al-Assad's resignation, it would be impossible "to fully stabilize" Syria.