Sen. Richard Blumenthal said Sunday he would urge Senate leaders to reconsider tougher gun control and mental health measures in the wake of this weekend's deadly shootings near the University of California, Santa Barbara. 

Appearing on CBS's "Face the Nation," the Connecticut Democrat said the recent shootings reminded him of the 2012 shootings at the Sandy Hook Elementary School in Newtown, Connecticut. after which "it seemed like we were on the verge of legislation that would stop the madness."

Those measures, which would include tougher background checks on gun sales and certain mental health initiatives, ultimately failed in Congress. But Blumenthal said he would urge lawmakers to "reconfigure" the bills to focus more on the mental health provisions, where he said there could be some agreement with Republicans.

Sen. John Thune (R-S.D.) said on the same program that it was important to have policies in place that allow people with mental health issues to be diagnosed and treated. "I think that's something on which there is agreement, and that's where we should be focusing our efforts," he said.