Rep. Peter T. King (R-N.Y.) said Sunday that Friday’s deadly rampage near the University of California at Santa Barbara underscores why expanded background checks for firearm sales are needed and said he hopes to pursue legislation to enhance mental health screening.

“This tragedy demonstrates once again the need to keep guns out of the hands of the mentally ill,” King said in an interview with The Washington Post.

King, who represents a suburban Long Island district and is one of the GOP’s most prominent gun-control advocates, also pushed Republicans to buck powerful gun rights groups.

“Even though this issue may not be popular in particular congressional districts, if we want to be a national party, we ought to be looking closely at it,” he said.

King and Rep. Mike Thompson (D-Calif.) introduced a bill last year that would extend background checks to include most private firearm transactions. It served as a companion bill in the House to similar legislation introduced by Sens. Patrick J. Toomey (R-Pa.) and Joe Manchin III (D-W.Va.).

The Toomey-Manchin bill failed in April 2013 after it was introduced as an amendment, getting the support of 54 senators when it needed 60 votes to move forward. The King-Thompson bill has not yet been brought to the House floor for a vote.

King said that because efforts to pass such legislation have fizzled, convincing House leaders to bring a bill up this summer will be “very difficult.” But he believes there should be more rigorous talks on Capitol Hill about mental health and firearm purchases.

“We’ve got to look at how we define mental illness, who is denied weapons and who is not, and focus the discussion,” he said. “We have to have this debate.”

King’s comments come as other political figures, including Sen. Richard Blumenthal (D-Conn.) and Education Secretary Arne Duncan, are calling for expanded background checks following Friday’s incident, in which 22-year-old college student Elliot Rodger killed six people, slaying three in a shooting rampage through the seaside community of Isla Vista. The other three were  found stabbed to death in his apartment, police said. The rampage ended when Rodger fatally shot himself in his vehicle, authorities said.

“Gun violence has no place anywhere, least of all at our nation's schools and college campuses, and we must do more to keep guns out of the wrong hands and increase access to mental health services,” Duncan said in a statement.

Blumenthal said Sunday on CBS's "Face the Nation" that he would like Congress to reshape last year’s gun-control bills and put a greater emphasis on evaluating the mental health of firearm buyers.

“Obviously, not every kind of gun violence is going to be prevented by laws out of Washington," he said. "But at least we can make a start, and I am going to urge that we bring back those bills, maybe reconfigure them, center on mental health, which is a point where we can agree that we need more resources to make the country healthier and to make sure that these kinds of horrific, insane, mad occurrences are stopped.”

Sen. Dianne Feinstein (D-Calif.) echoed Blumenthal in a statement, saying “shame on us for allowing this to continue.”

“We must ask ourselves if an individual whose family called police with concerns about mental health, who is receiving therapy and who has had several run-ins with police should be allowed to own multiple firearms and hundreds of rounds of ammunition,” she said. “When anyone, no matter their mental health or history, can so easily obtain any gun they want and as many as they want — we must recognize there is a problem.”

Speaking Saturday at a news conference, a grieving Richard Martinez, whose son, Christopher, was killed Friday near the UCSB campus, blamed gun-rights lobbyists and politicians for his son’s death.

“Why did Chris die? Chris died because of craven, irresponsible politicians and the NRA.,” Martinez said. “They talk about gun rights. What about Chris’s right to live? When will this insanity stop? When will enough people say: ‘Stop this madness. We don’t have to live like this?’ Too many have died. We should say to ourselves: Not one more.”