Durbin said the shooting raises several unanswered questions, including how a man with an apparent mental illness gained security clearance to enter the Washington Navy Yard, and how he gained access to weapons.
Nonetheless, Durbin said Congress should pass legislation aimed at limiting access to firearms for certain people.
"We've got to … do everything we can to keep guns out of the hands of those who would misuse them," he said. "Felons who would have a history of misusing firearms, the mentally unstable who can't be trusted to have a firearm."
Durbin gave a nod to language from Sens. Joe Manchin (D-W.Va.) and Pat Toomey (R-Pa.) that would have required criminal background checks at gun sales and over the Internet, a proposal that failed in the Senate earlier this year.
Durbin said most Americans think it's common sense to put some limits on gun ownership, and urged Congress to renew its effort to find a legislative proposal.
"God forbid we go on as business as usual," he said.