Durst, recently featured in the HBO documentary "The Jinx: The Life and Deaths of Robert Durst," must remain in Louisiana on local weapons charges at least until his next court date on April 2, Magistrate Judge Harry Cantrell ruled.
"There is a substantial risk the defendant might flee," Cantrell said.
Durst's lawyer, Dick DeGuerin, did not seek bail but argued his client's arrest and the search of his hotel room earlier this month in New Orleans were improper.
Durst's attorneys want to expedite his extradition to Los Angeles County, where he has been charged with the 2000 murder of longtime friend Susan Berman.
The HBO documentary broadcast evidence that Durst's handwriting appeared to match that of Berman's likely killer.
The 71-year-old Durst's voice was subsequently captured on a microphone saying to himself that he had "killed them all."
Long a suspect in the disappearance of his wife, Kathleen Durst, in 1982 in New York, Durst was acquitted in the dismemberment killing of his male neighbor in Texas in 2003.
The final HBO episode aired one day after Durst's arrest at a hotel in New Orleans, where he was staying under an assumed name and had in his possession more than $42,000 in cash, a revolver, a stash of marijuana and a latex mask that could fit over his neck and head, authorities have said.
FBI agents arrested Durst out of fear he would flee the country, an FBI spokeswoman has said.
Durst, who is long estranged from his powerful family with its major New York real estate holdings, appeared in court on Monday with what looked to be a newly shaved head.
James O'Hern, an investigator for the local district attorney's office, testified that authorities tracked Durst down after he placed two calls from a phone at the hotel to the voicemail on his personal phone.
They also found a piece of paper in his room with a tracking number for a package that authorities later seized and found to contain $117,000, O'Hern said.
Durst faces local charges of one count of possessing a gun as a convicted felon and one count of possessing a weapon with a controlled substance.