"I think that is the number one requirement. I also said that we should increase numbers of refugees.
"The administration originally said 10. I said we should go to 65, but only if we have as careful a screening and vetting process as we can imagine, whatever resources it takes.
"I do not want us to in any way inadvertently allow people who wish us harm to come into our country," Clinton said.
GOP presidential candidate Marco Rubio noted on Sunday that the Paris terrorist attacks are an example of why the United States should not admit more Syrian refugees.
"We won't be able to take more refugees. It's not that we don't want to, it's that we can't. Because there's no way to background check someone who's coming from Syria.
"You can have a thousand people come in and 999 of them are just poor people fleeing oppression and violence. But one of them is an ISIS fighter--if that's the case--you have a problem.
"There's no way to vet that out. There's no background check system in the world that allows us to find that out because who do you call in Syria to background check them?" Rubio said on ABC's This Week.