NEW YORK — Invoking the memories of Martin Luther King Jr. and Robert Kennedy, Mayor Michael Bloomberg on Monday urged Congress to make sure the system for background checks on firearms purchases includes the names of everyone prohibited from buying weapons and closes loopholes that allow some sales to take place without checks.

"We cannot wait any longer," said Bloomberg, an advocate for stronger gun control who helped create Mayors Against Illegal Guns. "We cannot turn our backs on this national calamity any longer."

Bloomberg was joined at City Hall by Martin Luther King III, as well as family and friends of those injured and killed in notorious shootings in Tucson, Ariz., at Virginia Tech and Columbine High School in Colorado. There also were people affected by killings that may have never made the news, like a host of New York parents who had lost children in shootings.

Federal law prohibits certain people, like convicted felons, drug abusers and the mentally ill, from being able to purchase firearms, and since 1993, a national background check system has been in place.

But that system is far from complete, Bloomberg said, because all the required records haven't been added to it, and Congress hasn't provided all the funding needed to make sure that happens. For example, he said 10 states haven't submitted any mental health records and 18 states have put in less than 100.

In addition, he said loopholes in the law exempt some gun buyers from undergoing background checks but requires it of others. For example, customers of licensed gun dealers must undergo background checks. But they're not required of those who buy from an "occasional" seller through places such as gun shows, or in private sales.

That creates an opportunity for people who might not pass a background check to still buy weapons.

Bloomberg called Congress should take action to fix those problems. He also said President Barack Obama should speak out on the issue at his State of the Union address this week.

"With our country still mourning the victims of Tucson, we believe it is an opportunity for our president to make a strong pledge to fix our gun laws and shore up our background check system because the state of our union includes the tragic reality that 34 Americans are murdered with guns every single day, and most of them are purchased or possessed illegally," he said.

TUCSON — Jared Loughner had trouble with the law, was rejected by the Army after flunking a drug test and was considered so mentally unstable that he was banned from his college campus, where officials considered him a threat to other students and faculty.

But the 22-year-old had no trouble buying the Glock semiautomatic pistol that authorities say he used in the Tucson rampage Saturday that left six dead and 14 injured, including Rep. Gabrielle Giffords.

Loughner's personal history did not disqualify him under federal rules, and Arizona doesn't regulate gun sales. His criminal charges were ultimately dismissed, the Army information was private and Pima Community College isn't saying whether it shared its concerns about Loughner with anyone besides his parents.

Loughner cleared a federal background check and bought the pistol at a big-box sports store near his home on Nov. 30 — two months after he was suspended by the college. He customized the weapon with an extended ammunition clip that would have been illegal six years earlier.

Gun-control advocates say the shooting shows that Arizona, home of some of the nation's most permissive gun laws, must review its laws to make sure firearms are not falling into the wrong hands. Gun-rights proponents disagree and say more regulation would not have stopped the tragedy.

Arizona eased gun restrictions last year when it passed a law allowing residents 21 and older to conceal and carry a weapon without a permit, which allowed Loughner to furtively — and legally — carry his pistol to the mall where he is accused of opening fire.

No permits or licenses are required at the state level. Legal gun owners can bring concealed weapons into Arizona bars and restaurants, and state legislators are considering allowing students and teachers to have weapons in schools.

After the shooting, Pima County Sheriff Clarence Dupnik berated Republican lawmakers who have sought to further ease state gun laws.

"I think we're the Tombstone of the United States of America," the Democrat said, referring to the Wild West town populated by gunslingers. "I have never been a proponent of letting everybody in this state carry weapons under any circumstances that they want, and that's almost where we are."

Charles Heller, co-founder and secretary of an Arizona group that promotes gun rights, said more regulation is not a solution.

"Why don't we ban murder? ... Murders are illegal and people do it anyway," he said. "There is no way to weed people out."

Outside Sportsman's Warehouse, the cavernous store where Loughner purchased his Glock, gun owner Jason Moats said that "the bad guys can get the guns either way." He suggested that the shootings could have been less tragic had there been one more weapon out there, rather than one less.

If someone at the mall was armed and had shot Loughner, ending the attack, "the guy would be a hero," said Moats, a 25-year-old route manager for a waste hauling company.

Eyewitnesses say Loughner was subdued after he tried to insert a second magazine into his pistol.

Karen Seaman, chief marketing officer for Sportsman's Warehouse, said Loughner passed a federal background check required to buy a gun.

Background checks are designed in part to weed out prospective gun buyers who have felony criminal records, have a history of domestic violence or are in the country illegally. None of that applied to Loughner, although the background check form asks about drug use and friends say he frequently used marijuana in high school.

In October 2007, Loughner was cited in Pima County for possession of drug paraphernalia, which was dismissed after he completed a diversion program, according to online records.

Loughner was arrested in October 2008 on a vandalism charge near Tucson after admitting that he vandalized a road sign with a magic marker, scrawling the letters "C'' and "X'' in what he said was a reference to Christianity. The police report said Loughner admitted other acts of vandalism in the area. The case was ultimately dismissed after he completed a diversion program.

A military official in Washington said the Army rejected Loughner in 2008 because he failed a drug test. The official spoke on condition of anonymity because privacy laws prevent the military from disclosing such information about an individual's application.

Last year, Pima Community College police were called in five times to deal with Loughner's classroom and library disruptions. He was suspended from the college in September after campus police discovered a YouTube video in which Loughner claimed the college was illegal according to the U.S. Constitution. School officials told Loughner and his parents that to return to classes he would need to undergo a mental health exam to show he was not a danger.

A college spokesman did not respond to an e-mail asking if the college had referred any information on Loughner to local police.

On Nov. 30, the same day he bought the Glock, Loughner posted a YouTube video that raged against the college and police.

"If the police remove you from the educational facility for talking then removing you from the educational facility for talking is unconstitutional," he wrote on the video. "The situation is fraud because the police are unconstitutional. ... Every Pima Community College class is always a scam!"

Federal law bars gun ownership for people who've been judged dangerously mentally ill by a court and those who have been committed to a mental institution, thresholds that didn't disqualify Loughner.

"It's not easy to draw that line" of when a person's mental illness should disqualify them from owning a weapon, said Michael J. Fitzpatrick, executive director of the National Alliance on Mental Illness, an advocacy group.

"The reality is most people with mental illness are not violent," he said. "The issue, frankly, is getting people into treatment. It's not about guns."

Daniel Vice, a senior attorney with the Brady Center to Prevent Gun Violence, said something should have prevented Loughner from buying a gun so easily.

"Here is a guy who couldn't enlist in the military and was kicked out of school. Anyone would tell you don't give this guy a gun," Vice said. He added that Loughner's problems might have been detected in other states that require more restrictive state permits, including New Jersey, Massachusetts, Hawaii and Illinois.

For example, Indiana can deny guns to anyone with documented evidence of violent or emotionally unstable conduct, a stricter standard than used federally. Vice said in Massachusetts, permits are issued not through store clerks but through police, who could bring greater scrutiny to who buys a gun.

Todd Rathner, a national board member for the National Rifle Association, chastised those clamoring for legislative changes with Arizona in mourning.

"It's unfortunate that some people are using this as an opportunity to talk about their political views," Rathner said. "There are people who haven't even had funerals yet, we have a well-liked congresswoman who is clinging to life."

Guns are entwined with Arizona's frontier heritage. Giffords is a gun owner, as was at least one of the six people killed, federal Judge John Roll.

Heller's group, the Arizona Citizens Defense League, is working on a bill that would provide firearms training for legislators and staff, and would even assign employees firearms confiscated in crimes for protection. "The criminal will always have a gun," Heller said.

Critics have faulted Arizona for the availability of guns. A report released in September by Mayors Against Illegal Guns, an association of more than 500 mayors, found that nearly half of the guns that crossed state lines and were used in crimes in 2009 were sold in just 10 states, including Arizona.

Loughner was able to buy an extended magazine that between 1994 and 2004 was prohibited under federal law, although many were in circulation prior to that time and remained legal. Sen. Frank Lautenberg, D-N.J., said in a statement Monday he will introduce a bill to ban high-capacity gun magazines.

"The only reason to have 33 bullets loaded in a handgun is to kill a lot of people very quickly," Lautenberg said in a statement.

Rep. Peter King, a New York Republican, is taking a different approach. He said he plans to introduce a bill that would make it illegal to knowingly carry a gun within a thousand feet of "certain high-profile" government officials.