One problem, the Pentagon chief told CBS News State Department Correspondent Margaret Brennan, is that the U.S. is seeking people who want to fight ISIS extremists but finding people who are more concerned about fighting Syrian dictator Bashar Assad.
"The numbers have been small so far because we have been selecting people in a very rigorous way. We have rules, which require us to vet fighters. And those rules are very principled, but they're stringent. And so not everybody passes. Only a fraction of the people who apply can pass that test," Carter said in an exclusive interview in Talinn, Estonia. "The other thing that limits their numbers is that we're looking for people who are willing to go after [ISIS] first, and there are many who would like to go after the government of Assad."
The U.S. has signaled that, for the time being, taking out ISIS in Syria is a more immediate objective than forcing Assad out of power. Brennan asked Carter whether he wants to change that policy.
"Our view is let's take on [ISIS] first," he replied. "And then of course we're hoping that Assad will be removed through a political process, a political transition, and we're working on that at the same time. So we're trying to get people who want to fight ISIL and who can pass U.S. vetting. And those numbers, so far, are small, but they are growing."
Carter also discussed the progress of recruitment efforts in Iraq, where the U.S. and its regional allies are trying to urge Sunni Muslims to take up arms against the insurgents in their midst.
"They haven't wanted to fight with the Iraqi security forces because they haven't believed that the government in Baghdad was supportive of Sunni aspirations," Carter said, blaming the sectarian divisions sown by the Shia-dominated government of former Prime Minister Nouri al Maliki. He commended the new prime minister, Haider al Abadi, for making progress in winning "the allegiance of Sunni forces so that there are capable and motivated Sunni forces again. Because they and only they can secure the defeat of [ISIS] in Sunni territory."
The Sunni recruits, Carter added, "are coming greater numbers now. In the coming weeks and months, we hope that continues."