The presumptive Democratic nominee restated on Monday her support for banning certain military-style weapons, like the one authorities say 29-year-old Omar Mateen used to kill 49 people in a weekend rampage.
Trump countered by exaggerating Clinton's proposal, saying erroneously that the former secretary of state has proposed abolishing the Second Amendment.
The real estate mogul boasted of his endorsement by the National Rifle Association, restated his call to ban foreign Muslims from entering the U.S. and criticized U.S. President Barack Obama's handling of the threat posed by Islamic terrorism.
Mateen, who was killed by authorities, was a 29-year-old American-born Muslim who worked as a security guard in Florida. He legally bought the weapons he used in the Orlando massacre.
Here's a look at the candidates' proposals on gun regulations.
Assault weapons ban
Clinton supports reinstating a federal assault weapons ban similar to what was enacted in 1994 under President Bill Clinton. That law expired 10 years later. In Cleveland on Monday, Clinton said: "We have to make it harder for people who should not have those weapons of war."
Speaking in New Hampshire a few hours later, Trump said Clinton's plans include "disarming law-abiding" citizens by "abolishing the Second Amendment and leaving only the bad guys and terrorists with guns."
Trump, in a reversal of positions he has taken before entering politics, supports no new restrictions on weapons or ammunitions.
On his campaign website, he calls such policies "total failures." He continues, "the government has no business dictating what types of firearms good, honest people are allowed to own."
Clinton supports requiring background checks on more kinds of gun purchases. Among them, the so-called "gun-show loophole" that exempts many sales made at gun shows from the existing FBI background checks required of potential gun buyers at retail stores.
A bipartisan bill to enhance background checks was rejected in the Senate in 2013 after the massacre of 20 children and six educators at an elementary school in Newtown, Connecticut.
Trump opposes any new restrictions. He says the current background check system could be improved upon and argues that criminals often obtain guns illegally.
It is not clear that changes to background checks would have made a difference in Orlando. Mateen legally obtained the two guns used in the shootings: an AR-15 style rifle and a handgun, according to the ATF. He held a security guard and statewide firearms license in Florida.
Beyond his insistence that gun control does nothing to curb violence, Trump has argued continually that more guns in circulation will make America safer.
He told CNN on Monday before his speech: "If you had guns on the other side, you wouldn't have had the tragedy that you had." Orlando police say an off-duty police officer at the club exchanged gunfire with Mateen after he'd begun his killing rampage.
Separately, Trump has called for ending "gun-free zones" around schools, arguing that would-be killers don't heed the rules. He later hedged, but said he'd like to see more armed officers and even trained teachers with guns on campuses.
Trump also calls for any state's concealed-carry permit to be accepted nationally.
Clinton said at a campaign event in Philadelphia in April that "we have just too many guns."
Trump and Clinton both call for beefing up mental health treatment, but Trump is more bullish about attributing mass shootings broadly to assailants with diagnosable mental health issues.
Trump on CNN called Mateen a "whack job."
Clinton wants to make it harder for people with mental health problems to purchase a gun. She described Mateen as a "madman filled with hate," but stressed that there was more to learn about the motives for the killings.
Mateen's ex-wife has said in media interviews that she believes he had bipolar disorder. But he has never been declared mentally ill by a court or otherwise diagnosed in any way that would have legally prevented him from obtaining the weapons police say he used at the Pulse club.
Gun makers' liability
Clinton has pledged to repeal a law that shields gun manufacturers from legal liability in gun deaths and she has pledged to provide more federal funding to increase inspections of gun stores.
During her primary race against Bernie Sanders, Clinton highlighted this position, arguing that she would be tougher than the Vermont senator on manufacturers and dealers.
The owner of the gun store where Mateen bought his weapons said Monday that he passed a full background check and that if he hadn't bought the guns from him, he would've purchased them somewhere else.
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