Four senators working on legislation to expand background checks for firearm purchases are not anywhere near an agreement, Sen. Tom Coburn said Sunday.

“I don’t think we’re that close to a deal, and there absolutely will not be record-keeping on legitimate, law-abiding gun owners in this country,” the Oklahoma Republican said. “And if they want to eliminate the benefits of actually trying to prevent the sales to people who are mentally ill, and the criminals, all they have to do is create a record-keeping, and that will kill this bill.”

Coburn has been working with Illinois Republican Mark S. Kirk, New York Democrat Charles E. Schumer and West Virginia Democrat Joe Manchin III on developing the narrower background check legislation, which aims to ensure that criminals and those with mental health issues are not able to access firearms.

If that working group reaches an agreement, the proposal could be among the most likely to become law in response to last December’s mass shooting at Sandy Hook Elementary School in Newtown, Conn.

“If you really want to improve it, you have to eliminate the record-keeping and give people the right and the responsibility to do the right thing and, that’s check on the [national] list to make sure you’re not selling a gun to somebody who is in one of those two categories,” Coburn said, in an appearance on Fox News Sunday.

A Senate aide familiar with the process said Fox News Sunday host Chris Wallace erred in the question he posed to Coburn. The aides said there is no discussion of allowing the federal government to keep any records of background checks or sales, something that is already illegal and would not change. What is being proposed is having the seller retain a record of a private sale, just as a dealer does now for a sale that happens at a licensed gun store, the aide said.

Schumer acknowledged that the negotiations are “challenging, as you’d expect on an issue as complicated as guns”

“But all of the senators involved are approaching this in good faith,” he added in a statement. “We are all serious about wanting to get something done, and we are going to keep trying.”

Coburn’s comments followed a speech Saturday by National Rifle Association CEO Wayne LaPierre in which he warned against implementation of universal background checks for firearm purchases, saying it is intended to create a national gun registry.

“Don’t you be fooled,” LaPierre said in Salt Lake City. “There is nothing ‘universal’ nor ‘reasonable’ about it. This so-called ‘background check’ is aimed at one thing — registering your guns. When another tragic ‘opportunity’ presents itself, that registry will be used to confiscate your guns.”

LaPierre then aired an NRA ad that featured an edited clip of Schumer calling background check and anti-gun trafficking measures under development “universal registration.” The New York Democrat is a longtime foe of the NRA.

“Let me say it here and now and for the world to hear — for once in my life, I agree with Chuck Schumer,” LaPierre said.

Senate Judiciary Chairman Patrick J. Leahy responded Sunday on CNN’s “State of the Union” that LaPierre’s comments were misleading.

“It’s not going to be registration,” the Vermont Democrat said. “And, of course, [LaPierre] knows that, but he’s paid very well to stir up his membership and help increase dues-paying members.”

Leahy noted that he comes from a state with many gun owners, but he said that people he talked to generally accepted the idea of records checks before buying weapons.

“I don’t think there should be exemptions at a gun show or for straw purchasers,” he said. “We want to say to everybody, so that if you have a violent crime in your background, if you’re under a restraining order, if you have some of these problems, you’re not going to be able to legally purchase a firearm.”