Perry said that "the last thing I want is the Texas Capitol to turn into DFW Airport," referring to security checkpoints that have become familiar features of airport terminals.
Fausto Cardenas remained in Travis County's jail Friday, charged with felony deadly conduct in the Thursday shooting. Witnesses said he fired gunshots into the air and was reloading when state troopers tackled him.
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Perry said enough people in Texas have concealed handgun licenses to deter violent criminals.
"That keeps us all safer," he said.
His comments came as he accepted the endorsement of the Texas State Rifle Association and the National Rifle Association.
Perry's in a tough fight with U.S. Sen. Kay Bailey Hutchison for the May 2 Republican nomination for governor.