WASHINGTON -- If someone admits to a federal official that he's used illegal drugs, that information should be sent to the FBI so that person can be disqualified from purchasing a gun, Sen. Chuck Schumer said Sunday.

Noting that the alleged shooter in the Tucson massacre had admitted to military recruiters that he had used drugs on several occasions, Schumer said he is proposing to the Justice Department and Bureau of Alcohol, Tobacco, Firearms and Explosives that the military be required to notify federal officials about such admissions. The New York Democrat said such a process does not require new legislation.

Jared Lee Loughner is charged with five federal counts in the killing of a federal judge and shooting of Arizona Rep. Gabrielle Giffords. The mass shooting January 8 outside a Safeway grocery store resulted in six dead and 13 injured.

A military official told Fox News last week that Loughner was rejected from enlisting in the Army in 2008 because he admitted he had used drugs. The official spoke on condition of anonymity because privacy laws prevent the military from disclosing such information about an individual's application.

Schumer said if military recruiters or other officials report admissions of drug use to a national database, those individuals could be denied a gun.

"After Jared Loughner was interviewed by the military, he was rejected from the Army because of excessive drug use. Now, by law, by law that's on the books, he should not have been allowed to buy a gun," Schumer told NBC's "Meet the Press."

"But the law doesn't require the military to notify the FBI about that, and in this case they didn't. So I --this morning -- I'm writing the administration and urging that that be done, that the military notify the FBI when someone is rejected from the military for excessive drug use and that be added to the FBI database," Schumer said.

The issue of limiting Second Amendment rights has exploded in the wake of the Arizona shooting as lawmakers and officials discuss whether increased curbs should be put on gun ownership.

Pennsylvania Gov. Ed Rendell said Sunday that a citizen protecting his home or hunting doesn't need a gun with 33 bullets per clip.

"I think the nation's spirits would be lifted if the Congress acted quickly with the president and reinstated the assault weapons ban which also had the ban on these large magazines, these clips that carried 30-plus bullets," he said.

Rendell, speaking on CBS' "Meet the Press," added that had Loughner earlier been classified as having mental illness, he would never have gotten a gun under provisions established in existing gun control laws.

"Had this man been classified, had he been committed civilly at any time prior to his purchasing the gun from Wal-Mart, he would have in fact been denied access to that firearm," Rendell told "Face the Nation."

Schumer said he is hopeful legislation would move to reinstate the assault weapons ban. But the senator noted that while the mental illness provision had been added to gun laws several years ago -- after a shooting in Long Island in which the gunman had been declared by a court as mentally ill -- Loughner was not on anyone's books because he apparently never received treatment.

Former New York Mayor Rudy Giuliani, who appeared with Rendell, said that some would argue that if more people had been carrying guns, the alleged shooter may not have gotten off as many rounds as he did. But, he added, Loughner apparently suffered from paranoid schizophrenia, which went untreated.

"The most important thing that would have prevented this is if this Loughner had been identified as what he clearly was," he said.

Sen. Tom Coburn, R-Okla., who appeared with Schumer, agreed that the law was not written with a case like Loughner in mind.

"There's a hole in what we need to do. And I'm willing to work with Senator Schumer and anybody else that wants to make sure people who are mentally ill cannot get and use a gun," he said.