But Clinton's running mate, Tim Kaine, says Trump's remark was inciting violence -- or "at a minimum, an expression of indifference to whether violence would occur."
"And this is a pattern that has been repeated over and over again, and I think this doesn't belong in any race, much less a race to be president of this country," Kaine said.
The two vice presidential nominees jousted over what Trump had meant in separate Sunday show interviews.
Kaine condemned Trump in an interview with Chris Wallace on "Fox News Sunday." And Pence defended his running mate on ABC's "This Week" with Martha Raddatz.
Asked what Trump meant by that remark, Pence said: "Well I think, you know, Donald Trump believes in the safety and security of every American, and any suggestion otherwise regarding Secretary Clinton is just nonsense. "
Pence then appeared to claim Clinton "has had private security" for the last 30 years, which is false. She's been protected but the US Secret Service since Bill Clinton's campaign for the presidency in 1992. The Secret Service is part of the federal government and protects presidential and vice presidential candidates in both parties, as well as their families, and visiting heads of state. It is not a private security force.
"I mean, the point that he was making is that Hillary Clinton has had private security now in her life for the last 30 years, but she would deny the right of law-abiding citizens to have a firearm in their home to protect their own families. I think what Donald Trump was saying is that if Hillary Clinton didn't have all that security, she'd probably be a whole lot more supportive of the Second Amendment," Pence said.
Pence also complained about being pressed about Trump's comments, saying news media focus too much on the GOP nominee's controversial utterances.
"You know, I just joined this campaign a couple months ago. But, you know, to be honest with you, Martha -- I have a lot of respect for you. But a lot of people in the national media spend more time talking about what Donald Trump said in the last day than they do talking about what the Clintons have been up to for the last 30 years," Pence said.
Kaine, meanwhile, pointed to Trump's history of appearing to raise the possibility of violence against Clinton.
Trump had said last month in North Carolina that there would be nothing conservatives could do if Clinton was elected and could appoint her own Supreme Court justice, before adding, "although the Second Amendment people -- maybe there is, I don't know."
"What did that mean when he said that just three weeks ago?" Kaine said. "And when you look at a series of these comments that he's making, I do believe it is an (incitement) -- or at a minimum, an expression of indifference to whether violence would occur."