Washington (CNN) Republican presidential contenders have largely called for increases in surveillance in the wake of terrorist attacks in Paris and California. But they also argued Sunday that one U.S. surveillance tool -- the government's no-fly list -- can't be trusted as a tool to bar gun purchases.

Several GOP candidates for the 2016 presidential nomination argued against a Democratic push to bar members of the no-fly list from buying firearms during appearances on Sunday news shows, saying that list is too broad. Just one -- Donald Trump -- said they were willing to consider the move.

"The majority of the people on the no-fly list are often times people that just basically have the same name as somebody else who doesn't belong on the no-fly list. Former Sen. Ted Kennedy once said he was on a no-fly list. There are journalists on the no-fly list," Florida Sen. Marco Rubio told CNN's Jake Tapper on "State of the Union."

Hillary Clinton launched her presidential bid on April 12 through a video message on social media. The former first lady, senator and secretary of state is considered the front-runner among possible Democratic candidates."Everyday Americans need a champion, and I want to be that champion -- so you can do more than just get by -- you can get ahead. And stay ahead," she said in her announcement video. "Because when families are strong, America is strong. So I'm hitting the road to earn your vote, because it's your time. And I hope you'll join me on this journey."

Ohio Gov. John Kasich joined the Republican field July 21 as he formally announced his White House bid. "I am here to ask you for your prayers, for your support ... because I have decided to run for president of the United States," Kasich told his kickoff rally at the Ohio State University.

Ohio Gov. John Kasich joined the Republican field July 21 as he formally announced his White House bid. "I am here to ask you for your prayers, for your support ... because I have decided to run for president of the United States," Kasich told his kickoff rally at the Ohio State University.

Sen. Ted Cruz of Texas has made a name for himself in the Senate, solidifying his brand as a conservative firebrand willing to take on the GOP's establishment. He announced he was seeking the Republican presidential nomination in a speech on March 23."These are all of our stories," Cruz told the audience at Liberty University in Virginia. "These are who we are as Americans. And yet for so many Americans, the promise of America seems more and more distant."

Businessman Donald Trump announced June 16 at his Trump Tower in New York City that he is seeking the Republican presidential nomination. This ends more than two decades of flirting with the idea of running for the White House."So, ladies and gentlemen, I am officially running for president of the United States, and we are going to make our country great again," Trump told the crowd at his announcement.

"I mean, Ted Kennedy and Stephen Hayes the journalist and Cat Stevens -- I mean, this is not a list that you can be certain of," Bush said. "If the FBI knows that someone's in our country and they're tracking them, they shouldn't be able to get guns for sure. But the no-fly list is a much broader list. It's not an accurate list to be able to use for restricting gun rights for law-abiding citizens."

And while Ohio Gov. John Kasich said that the United States could "probably keep (no-fly list members) from getting guns and ought to ban them," he's opposed to using other terrorist watch lists in restricting gun purchases.

His reasoning: Barring a terror suspect from buying a gun would tip that person off to the government's surveillance efforts.

"We want to make sure that we can exploit all the information that we possibly can get," Kasich told Tapper on "State of the Union." "So if all of a sudden you tell everybody who's on the watch list that you can't do this or that, then guess what happens? Then we lose our ability to track, we lose our ability to gather information, so I think we have to be careful."

Donald Trump, the GOP front-runner, appeared to differentiate himself from the rest of the field by saying he would consider supporting efforts to prohibit firearms purchases for no-fly list members.

"Well, I'd certainly take a look at it. I would," Trump said on CBS' "Face the Nation." "I'm very strong into the whole thing with Second Amendment -- but if you can't fly, and if you've got some really bad -- I would certainly look at that very hard."

Still, he said, in mass shootings, more gun owners could prove helpful.

"I'm a big believer in the Second Amendment," Trump said. "In Paris, they had no guns. In California they had no guns. Only the bad guys had the guns. So they were like sitting ducks, every one of 'em."

"People who have been barred from flying on airplanes should not have guns," Vermont Sen. Bernie Sanders said on CBS' "Face the Nation."

That drew criticism from Republicans who said their focus on guns was misplaced.

"The first impulse of Hillary Clinton and Barack Obama is to have gun control," Bush said Sunday. "But the first impulse in my mind is let's have a strategy to take out ISIS there so we don't have to deal with it here."

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But Clinton pushed back, calling for "unity about how we prevent terrorist attacks and how we prevent the wrong people from getting a hold of guns."

She said she understands the concern that some members of the no-fly list have done nothing wrong.

"That's why there's a process for people to be able to raise their concerns about being on the list and then to have a process that could even lead to a legal action to remove yourself from the list," Clinton said.

But, she added: "I took the shuttle from New York. I'm a lot happier having a list that keeps people off planes that there's any question about their intent or their potential behavior."

And former Maryland Gov. Martin O'Malley tweeted his support for a New York Times editorial calling for gun control reforms, saying he supports the use of executive orders to accomplish them.

I agree—this is a "moral outrage & nat'l disgrace." If Congress doesn't have courage to act, let's use EOs. -O'M https://t.co/eIct6AlAKw — Martin O'Malley (@MartinOMalley) December 5, 2015

"I agree—this is a "moral outrage & nat'l disgrace." If Congress doesn't have courage to act, let's use EOs. -O'M," he tweeted.