Beshear said Wednesday's violence forces a question on leaders across the country, no matter their party affiliation.
"Violence is never the answer. Ever. And I hope that every leader out there will answer the question whether they believe violence is the answer ever or violence is never the answer if directed toward people like them," he said. "It's got to be the first if we are going to continue to be the great country that we are."
The comments struck a different tone from a video message released by President Donald Trump, who pointed to the effects of demonizing people with whom one disagrees but singled out rhetoric on the "radical left" for the act and did not include Democratic politicians who have been targeted.
Without referring to Trump, Beshear told reporters Thursday that leaders can't "fan the flames and condemn the fire."
"What I'd like to see is leaders on every side condemning the type of speech that just goes too far, that suggests that one group of people aren't American or don't deserve to be here or incites violence in different ways," he said. "I'd like to see us speak out against all of that."
The governor linked the comments to his remembrance of 9/11, urging Kentuckians to recall the sense of unity in the days that followed the terrorist attacks.