Sen. Chris Murphy (D-Conn.) on Sunday conceded that a federal ban on assault rifles is unlikely because of a lack of congressional support but pushed for lawmakers to consider a bill that would require training before purchasing such a weapon.

"There's not the votes to do that," Murphy said of an assault weapon ban on CBS's "Face The Nation." "Ultimately, I want those weapons off the street. But I think we’d be a safer nation if we required just a little bit of training before you bought the most dangerous weapons commercially available."

Murphy, who has been a proponent of a national assault weapon ban, is pushing for enhanced training requirements following the shooting at a private Christian school in Nashville, Tenn. earlier this month that left three students and three adults dead. 

"I just don’t understand why we choose to live like this," Murphy said on CBS. "Why we choose to make our kids fear for their lives when they walk into their schools."

The debate over gun control and the remedies needed to stop mass shootings in the U.S. have hit familiar drags in Congress, with Democrats and Republicans not finding common ground not only on what the solution for the problem is, but also its root causes.

The shooter in Nashville entered the school with two assault-type weapons and a handgun. Murphy said on Sunday that he wants to make it so that the type of weapons that were used in the attack only end up in the hands of responsible owners. He also renewed a call for universal background checks.

"What if we said before you get an AR-15, you have to show that you are responsible, that you know how to operate it, what if we applied background checks universally, simply to the purchase of those weapons?" Murphy asked.

Murphy also pointed to the bipartisan gun control legislation that was passed in the aftermath of the school shooting in Uvalde, Texas, last year as a sign of hope that lawmakers could get something done.

"Things change pretty quickly in Washington," Murphy said. "And my goal is to try to find that common ground that [Sen.] John Cornyn [R-Texas] is talking about… We’ve got to show parents and kids and families in this country that we can make bipartisan progress, to try to make our country safer."