Flake, speaking on the ABC News program "This Week" Sunday said everyone wants a more civil society.
"Well, every time there's a shooting like this or something like this happens, that debate comes up," Flake said. "Sometimes statements are made that are dialed back later because it turns out that the motive wasn't what people assume. And so I think you have to be careful there."
Police arrested Jared Lee Loughner, a 22-year-old Tucson college dropout who has posted rambling comments on the Internet, in the shootings. They were looking for a second man they think might be involved in Saturday's shootings.
Also appearing on the program was Rep. Chris Van Hollen, D-Md. He said people need to find a way to disagree without violence.
"I think this is a moment for all of us in Congress, all of us in the country, all of us in media to reflect on where we are today in the debate," Van Hollen said.
"I think it's very fitting and appropriate that Speaker (John) Boehner has decided to suspend activities in the House of Representatives in the coming week so that we can all take a little time to figure out how we move forward as a Congress and, I think, in the country at large."