Since the shooting, a number of legislators, including some with "A" ratings from the National Rifle Association, have called for action on guns. Sen. Dianne FeinsteinDianne FeinsteinA guide to the committees: Senate Dem: Trump's China trademark looks like a quid pro quo Senate advances Trump's Commerce pick MORE (D-Calif.) plans to introduce a new federal ban on assault weapons bill in 2013. Other legislators have said they plan on introducing legislation outlawing high-capacity gun clips. Portman, who voted against a 1994 assault weapons ban, said "both of those topics ought to be looked at."

"It's important that we look at this carefully, logically and understand what the trade-offs are. I'm a supporter of the Second Amendment," Portman added. "I am always concerned that we go too far with restricting rights when there is not a good case to be made [that] it will make us safer, but I'm open to looking at that issue."

Portman also said efforts on improving mental health policies should be considered, citing a number of other shootings over the past few years where the respective shooters reportedly suffered from mental disorders.

"That is the common thread you see in these shootings," Portman said. "These [gunmen] tend to be people who have fallen between the cracks or have been in the mental health system in a way that didn't keep them from getting access to guns. And there's more and more evidence that this is an issue that needs to be addressed."