WASHINGTON - Every day, a computer at the sprawling FBI crime information center in rural West Virginia kicks out the names of 100 or more convicted felons and others who, though barred by law from owning a gun, tried to buy one anyway by lying on their firearms application.

In most instances, the federal government knows where to find these gun-law violators, and has in its possession evidence that could lead to their convictions. But this is one gun law that the government rarely prosecutes.

The Clinton administration says it does not have the staff to pursue many cases, and is instead focusing on more serious crimes, but that assertion has triggered criticism from Republicans and pro-gun groups.

"It takes a lot of nerve to bang your fist and demand tougher juvenile gun laws while doing nothing to enforce the ones that already exist," said Rep. Bill McCollum (R., Fla.), a former federal prosecutor who has held hearings on the issue. "I must point out that doubling the size of the criminal code will not matter if the Clinton-Gore administration refuses to vigorously enforce these laws."

The administration counters that the gun-control law has accomplished its main purpose by preventing felons from buying guns legally.

The issue figures to play a central role in the congressional debate later this month on proposals by the White House to restrict gun sales to juveniles and to impose background checks on all sales at gun shows.

While shootings at Columbine High school in Colorado on April 20 and at a Jewish day-care center in California on Aug. 10 have added impetus to the gun-control movement, pro-gun groups point to the small number of prosecutions for violations of the Brady Act, the 1993 law that required background checks.

People who supply false information when applying to buy a firearm are flagged every day by the National Instant Check System, an FBI computer that gives gun store owners instant access to criminal records and other information to find out whether a potential buyer is qualified to purchase a weapon.

Any purchaser who falsely denies that he has a felony arrest record or is under indictment or has anything else in his background that would disqualify him from owning a weapon is subject to up to 10 years in federal prison upon conviction.

The Clinton administration says it prosecutes only a handful of those cases because the offenders often are not dangerous and because a higher priority is to go after illegal weapons traffickers who use straw purchasers with clean records to buy guns.

But failing to make those arrests can have horrible consequences. The most notorious example is that of Benjamin Nathaniel Smith, who killed two people and wounded nine in July in a racially motivated rampage in Illinois and Indiana before taking his own life.

As he planned the shooting, Smith first sought to buy a weapon from a gun store, but was turned down after the instant check disclosed that his ex-girlfriend had obtained a protective order against him. But no attempt was made to arrest Smith, and he later procured weapons from a private dealer selling guns from his home.

"He was identified during the check as a prohibited person, and in the end there was no follow-up," said Bill Powers, a spokesman for the National Rifle Association.

The NRA has gotten some support on that point from its arch-opponent, Handgun Control. The group's president, Bob Walker, says that while there may be other kinds of gun crimes, such as trafficking, that ought to get more attention from the government, there also ought to be more enforcement of the Brady law.

"There is certainly value in prosecuting people who lie" on a firearms application, Walker said.

The federal statistics on prosecutions for filing false information on firearms applications suggest a weak effort.

Of the 23,000-plus cases referred by the FBI to the Bureau of Alcohol, Tobacco and Firearms for potential prosecution since the beginning of the year, 65 people have been arrested, according to the ATF.

The State of Virginia alone prosecutes three times as many people under its program than the entire federal government.

But federal law enforcement officials say many Brady law violations involve people who are not dangerous, such as illegal immigrants or people who have been convicted of nonviolent crimes. And with limited resources, they argue, it makes sense to focus efforts on gun traffickers and felons who already have guns and are committing crimes with them.

The Justice Department contends that overall prosecutions for gun law violations have gone up 22 percent since 1992, when state cases are added to the mix.

To some extent, the Clinton administration is a victim of its own success. Since the NICS computer network went into effect last Dec. 1, about 100,000 people have been denied firearms.

The Justice Department says that fact alone shows the law is working, because dangerous criminals have been barred from purchasing guns.

"You have to take into account the number of people who have not had access to guns as a result of this system," said Deputy Attorney General Eric H. Holder Jr. "We have prevented people - stalkers, fugitives, felons, people who have domestic violence complaints lodged against them - from getting access to guns."

Prosecuting every Brady law violation, federal officials say, would quickly overwhelm the judicial system.

"I only have a dozen federal prosecutors in Richmond, and we have major drug-conspiracy and public-corruption cases," among others, said Helen Fahey, the U.S. attorney in Richmond, Va. "To do a couple of hundred Brady cases would consume the entire staff."

Because of such tight staffing, federal law enforcement officials say, they focus instead on gun traffickers and people who use guns in violent crime.

That is the case in Philadelphia, where, since January, the U.S. Attorney's Office has won indictments of 215 people on a variety of gun-related charges under a coordinated assault on gun violence, a 400 percent increase over the same period last year. But only a handful of those have been for false firearms applications.

"We have to prioritize our investigations," said Thomas Stankiewicz, head of the firearms trafficking task force for the ATF in Philadelphia. "Obviously the important investigations are of the people who are buying the guns and putting them in the hands of criminals. That's not to say that these [Brady law] cases are not being done, but they are not the top priority."

The State of Virginia aggressively goes after weapons buyers who provide false information. It was the first state in the country to begin computerized background checks when it began its program in 1989. Until then, Virginia's reputation for lax enforcement of firearms laws made it a magnet for weapons traffickers. But since the start of the program, authorities have made 3,883 arrests, with an 85 percent conviction rate, according State Police Capt. Lewis Vass.

In virtually every case where a person files false information, he said, Virginia authorities seek to make an arrest. The state is no longer known as a favorite destination for illicit weapons dealers.

"If someone was out there violating the law, we always felt it was our duty to bring that illegal activity to an end," Vass said.

Later this month, Congress goes back to work on a proposal to require background checks for all firearms purchases at gun shows. While federally licensed gun dealers are required to perform such checks, people who make sales from private collections are under no such obligation.

Critics of the current system say that gun shows have become a leading source of guns for criminals who would otherwise be turned down at stores after a background check.