Washington (CNN) Democratic Sen. Chris Murphy said Sunday that the effort to stem mass shootings like the one in Parkland, Florida, needs to go beyond focusing on law enforcement and encompass a comprehensive approach to gun control and mental health.

"You can't suppose every single time that you're going to be able to intervene before the shooter walks into a school with a military-style assault weapon," Murphy, a Connecticut Democrat, said on CNN's "State of the Union" Sunday morning when asked what he thought about the law enforcement response to the Marjory Stoneman Douglas High School shooting last week.

During the mass shooting at the Parkland, Florida, high school, one of the Broward County deputies waited outside the building and later resigned after being suspended without pay for his actions.

Murphy also acknowledged that the gunman in Parkland exhibited several warning signs that were flagged to law enforcement officials.

"There clearly are a lot of questions that need to be answered about why law enforcement didn't step in earlier in Florida. But there are just as many of these shootings that look like Sandy Hook, where there were no red flags," the senator said.

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