Jindal went on to say that it is important that existing gun laws are followed, reiterating that the shooter, 59-year-old John Russell Houser, should not have been allowed to purchase a gun because of his mental illness.
"I think every state should strengthen their laws," Jindal said. "Every state should make sure this information is being reported in the background system. We need to make sure that background system is working. Absolutely, in this instance, this man never should have been able to buy a gun."
Former Texas governor Rick Perry (R), another presidential candidate, echoed that sentiment, adding that he opposes the idea of "gun free" zones in part because they prevent law-abiding gun owners from stopping attacks such as the one in Lafayette.
"We see individuals who were obviously mentally impacted. These were individuals who, I think, that somewhere, somebody didn't do their job in the standpoint of enforcing the laws that are only on the book," Perry said on CNN's "State of the Union." "I will suggest to you that these concepts of gun-free zones are a bad idea. I think that you allow the citizens of this country who have been appropriately trained, appropriately backgrounded, know how to handle and use firearms to carry them."
Speaking on NBC's "Meet the Press," Sen. Bernie Sanders (I-Vt.), who is running for president as a Democrat, called for some new gun laws — suggesting that some assault weapons should not be sold in the United States and that the "gun show loophole" should be closed. Current background-check laws, he added, need to be properly enforced.
"Nobody should have a gun who has a criminal background, who's involved in domestic abuse situations. People should not have guns who are going to hurt other people, who are unstable," Sanders said. "We need a system that works. Bottom line is, I hope that nobody in America disagrees that people, as in the case of the shooting here in Louisiana, who have a history of mental instability should not be having guns. People who have criminal backgrounds, people who are abusing wives or girlfriends should not be having guns. That is the issue that, I think, we can bring people together around."
Real estate mogul and reality TV star Donald Trump insisted that the response to the shooting should be a conversation about mental illness, not about gun laws.
"These are sick people. I mean, these are very, very sick people," Trump, who is atop the Republican 2016 field in some national polls, said on CNN. "This has nothing to do with guns. This has to do with the mentality of these people."