Sen. Charles E. Grassley (R-Iowa), the ranking Republican on the Senate Judiciary Committee, said he welcomes his committee’s discussion of what to do after the mass shooting in Newtown, Conn. But he made clear: "The problem is greater than guns alone."

Seeking to steer the debate beyond recent proposals on gun control, Grassley noted that society as a whole is more corrosive, that the government should do more to bolster mental health programs and that video game manufacturers may also hold some blame.

"I share Vice President Biden’s disbelief of manufacturer denials that these games have no effect on real-world violence," Grassley said.

He was referring to recent White House meetings the vice president had with entertainment executives, who pushed back against suggestions that violent video games played a role in inspiring recent shootings.

"Above all, we should not rush to pass legislation that will not reduce mass killings," Grassley added. "Banning guns based on their appearance does not make sense. The 1994 assault weapons ban did not stop Columbine. The Justice Department found the ban ineffective. Scholars have indicated that refining or expanding such legislation will not cut gun violence."

Grassley was referring to Clinton-era Department of Justice studies that found that the 1994 assault weapon ban had not helped drive down the rate of violent crime – a point disputed by congressional Democrats.

Grassley also expressed skepticism of proposals to limit the size of ammunition clips, noting that any such proposals "can be circumvented by carrying multiple guns, as many killers have done."

"We hear that no one needs to carry larger magazines than those that hunters use to shoot deer,” Grassley added. "But an attacking criminal, unlike a deer, shoots back."

Despite his concerns with those proposals, Grassley said he believes there is room for agreement on passing laws that would make gun trafficking a federal crime.

Sen. Patrick J. Leahy (D-Vt.) has proposed such legislation and Sens. Kirsten Gillibrand (D-N.Y.) and Mark Kirk (R-Ill.) unveiled a similar bill Wednesday – the first bipartisan proposal addressing gun violence introduced since the Newtown shootings.