Prosecutors have not said whether they will bring those charges before a grand jury.
None of Durst's previous convictions was serious enough to merit the felon in possession charge, his attorneys say.
Durst was arrested at the J.W. Marriott Hotel. He had registered there under the name Everette Ward, and a search of his hotel room turned up his passport, nearly $43,000 in cash, a gun and a rubber or latex mask that could cover his head and neck, according to a search warrant for his Houston condo.
Durst, a member of a wealthy New York real estate family, was charged with murder in California for the December 2000 shooting death of Susan Berman.
He was arrested one day before the finale of "The Jinx," the show about his links to his first wife's disappearance in 1982; the death of Berman, a mobster's daughter who acted as his spokeswoman after his wife went missing; and a 71-year-old neighbor in Texas whose dismembered body was found floating in Galveston Bay in 2001. Durst has been tried only for the Texas killing, and he was acquitted of murder.
Durst waived extradition in New Orleans but is being held on the weapons charges.
Since early last week, he has been kept in the parish jail's mental health unit because jail officials say he's at risk for suicide. The Orleans Parish Sheriff's Office leases space in a prison 70 miles away under a federal court order to improve conditions at the jail.
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JANET McCONNAUGHEY, Associated Press
After nearly a week in a prison's mental health unit, millionaire Robert Durst — accused of killing a female friend in California 15 years ago — has a bond hearing scheduled Monday in New Orleans on weapons charges.
The 71-year-old's lawyers say his arrest was orchestrated to coincide with the last episode of an HBO show about him and his links to three killings. At Monday's bond hearing on the weapons charges, his lawyers want their client released; prosecutors want no bond allowed.
Durst's lawyers say he illegally arrested March 14 at a New Orleans hotel on both the weapons charges and on the Los Angeles County warrant accusing him of murder.
Lawyers William Gibbens and Dick DeGuerin outlined their arguments in court papers filed last week. One of the weapons charges alleges that he had a .38-caliber revolver; previous felony convictions make that illegal. The other charge alleges he had the weapon and illegal drugs: more than 5 ounces of marijuana.