Alexander's comments come as legislators debate strengthening gun laws in response to a shooting massacre at Sandy Hook Elementary School in Newtown, Conn., in December. The shooting left 28 dead including 20 children.
On Wednesday, former Rep. Gabrielle Giffords (D-Ariz.), the target of a mass shooting in Tucson, Ariz., in early 2011, appeared at a Senate Judiciary Committee hearing on gun violence.
"Speaking is difficult, but I need to say something important," Giffords, who suffered a gunshot wound to the head, said at the hearing. "Violence is a big problem. Too many children are dying. Too many children. We must do something."
Wayne LaPierre, the executive vice president of the National Rifle Association, also appeared before the committee. LaPierre argued against new gun restrictions, saying more strict background checks for gun purchasers "will never be universal, because criminals will never submit to them."