Mark Kelly, the husband of former Rep. Gabrielle Giffords (R-Ariz.), on Sunday warned GOP lawmakers not to filibuster efforts to pass gun control in the Senate.

"It is important to take action and the American people are demanding action now," said Kelly on “Fox News Sunday.” 

Kelly’s comments came in response to five Senate Republicans — Sens. Marco RubioMarco Antonio RubioTrump replaces McMaster with Bolton as national security adviser Orlando March for Our Lives protesters to march to Rubio's downtown office, Pulse nightclub Lawmakers eye crackdown on China’s Confucius Institutes MORE (Fla.), Rand PaulRandal (Rand) Howard PaulSenate approves .3 trillion spending bill, sending to Trump GOP senator threatened to hold up bill over provision to honor late political rival: report Conservatives balk over funding bill ahead of shutdown  MORE (Ky.), Ted CruzRafael (Ted) Edward CruzConservatives balk over funding bill ahead of shutdown  Confirmation fight over Trump pick exposes blurred lines in GOP-LGBT activism GOP pushes to change Senate rules for Trump MORE (Texas), Mike LeeMichael (Mike) Shumway LeeConservatives balk over funding bill ahead of shutdown  Overnight Defense: Senate sides with Trump on military role in Yemen | Dem vets push for new war authorization on Iraq anniversary | General says time isn't 'right' for space corps Senate sides with Trump on providing Saudi military support MORE (Utah) and James InhofeJames (Jim) Mountain InhofeHouse members urge Senate to confirm Trump's NASA nominee Senators to Trump: Keep pressure on North Korea while exploring talks Why did this administration back the Palestine Liberation Organization in terrorism case? MORE (Okla.) – who said last week that they will filibuster any additional gun restrictions, as Senate Majority Leader Harry ReidHarry Mason ReidGOP pushes to change Senate rules for Trump Trump presses GOP to change Senate rules Only thing Defense’s UFO probe proves is power of political favors MORE (D-Nev.) prepares to move a gun bill.

Kelly said that the bill, which expands background checks at its core, along with measures to punish straw purchasers of firearms and provide more funds for school safety, was supported by the public.

"They should listen to their constituents and certainly shouldn't be getting in the way of the process, which is to debate the bill and to vote on the bill," Kelly said.

"It doesn't make any sense and I imagine that at some point, if they actually do this, their constituents will hold them accountable for those actions," he added.

The former astronaut has been at the forefront of the issue since his wife was shot in the head more than two years ago.

Kelly said that 94 percent of Rubio's constituents support a universal background check, while 83 percent in Kentucky back the concept.

The bill includes language crafted by Democratic Sen. Charles SchumerCharles (Chuck) Ellis SchumerAmtrak to rename Rochester station after Louise Slaughter Conscience protections for health-care providers should be standard Pension committee must deliver on retirement promise MORE (N.Y.) after efforts to craft a bipartisan proposal on background checks faltered amid GOP concerns that the measure could lead to a federal database of gun owners. 

Kelly acknowledged the difficulties finding GOP support, but said he was optimistic an accord could be reached. "This is certainly an issue that can be worked on," he said.

"We have a lot of smart members in the Senate and I think they can figure out a compromise on this issue."

Kelly called expanded background checks "the most commonsense thing we can do to prevent criminals and the mentally ill from gaining access to firearms."

Kelly said 40 percent of all gun purchases happen without a background check and those sales could account for many of the weapons which fall into the hands of the mentally ill or criminals.

"It's crazy that we have this system where responsible owners get a background check and the option to avoid one is available for anybody who doesn't want to do it. It's a crazy system," Kelly said.

He demanded that any bill produced by the Senate apply background checks to purchases made at gun shows and through private sellers, including the Internet.

"The system currently works with federally licensed firearms dealers so there is no reason that same system can't work with the gun show and the private seller," he said.

While Republicans have expressed opposition to broader background checks, there is a push by a bipartisan group of senators to ensure that mental health information is submitted into the system and can be used by gun sellers.

Kelly acknowledged that the National Rifle Association (NRA) has a point when it argues that the current background check system is ineffective without a beefed up system that includes better access to mental health information and other records.

"They absolutely have a point they are right on that issue," he said. "We need to encourage states to include the mental health records."

In fact, under an improved system, Kelly argued, wife's shooter Jared Loughner would have been turned down from making a purchase.

He vowed to work with the Senate to reach a compromise on language that ensures that the legislation doesn't create of a national registry, which some opponents argue would lead to gun confiscations. He said records would remain at a gun store and would not be registered with the federal government.

Sen. Chuck GrassleyCharles (Chuck) Ernest GrassleyGrassley on Trump calling Putin: 'I wouldn't have a conversation with a criminal' Lawmakers zero in on Zuckerberg GOP senator blocking Trump's Intel nominee MORE (R-Iowa) is crafting an alternative Republican gun control bill that would not include a universal background check but would crack down on gun trafficking and beef up school safety.

Even though support for broader legislation has slipped somewhat since the Newtown massacre in December, Kelly argued that a majority of people — 92 percent of those polled overall and 74 percent of NRA members — want, at the very least, stricter background checks.

"I would hope, at some point, that the leadership of the NRA would just listen to their membership on this issue," he said.

While Kelly said the NRA has done a good job of controlling the debate "one thing that is different now is the fact that we had 20 first-graders murdered in a classroom along with six educators. That's unacceptable."