The star receiver, wearing a gray suit and a light blue shirt, arrived at Manhattan Criminal Court in the company of his wife and his attorney, Benjamin Brafman.
Both sides agreed to adjourn the case to June 15 following a brief hearing before Judge Michael Yazinsky. Burress' bail was continued.
Prosecutor John Wolfstaetter told the judge that the prosecution was continuing its investigation.
Brafman told reporters after the hearing that he had reached no plea agreement with prosecutors and said discussions were continuing. If the two sides agree, they will not necessarily wait for the scheduled court date, he said.
"If the case needs to be advanced to an earlier date it will be ...We are continuing to work our respective investigations, stay tuned," he said.
Asked whether Burress would play for the Giants this year, Brafman said, "It's not my decision. It's the Giants' decision and Plaxico's decision. It's not a legal decision, it's a sports decision.
"I assume a lot will depend on how, when and if this case is resolved and June 15th is the next day we are back unless there is a reason to come back earlier."
A law enforcement official with knowledge of the case said Monday that Burress' attorneys and prosecutors remain at odds over the terms of a plea deal, with the District Attorney's office pushing for a stiffer punishment than what defense lawyers believe Burress deserves.
Burress is charged with criminal possession of a weapon in the second degree, a felony carrying a minimum prison sentence of 3½ years upon conviction.
A plea deal that includes jail time, depending on the length of the sentence, could have a bearing on whether Burress is able to play football next season.
Statistics show that more than eight out of 10 people arrested in the city last year on the same charge Burress faces received reduced charges, though some plea deals included jail time.
Only about 14 percent of the people charged last year with the same charge that Burress faces were ultimately convicted of it, said John Caher, a spokesman for the state Division of Criminal Justice Services.
Of the 1,248 people in New York City initially arrested on second-degree criminal weapons possession in 2008, 184 were convicted of the charge. About half were convicted of a misdemeanor or violation, and the remaining convictions were usually lesser felonies with some jail time.
Prosecutors, in offering reduced charges in gun possession cases, consider past criminal history, arrest circumstances and the reason for having the weapon.
The 31-year-old wide receiver, who caught the winning touchdown pass in the Giants' 2008 Super Bowl victory over the previously undefeated New England Patriots, has no criminal record. The gun he was carrying had a Florida license that only recently expired; it wasn't licensed in New York.
Burress has not spoken publicly about why he was carrying a gun, but some have speculated it was for safety reasons after teammate Steve Smith was robbed at gunpoint three days before the incident.
Former prosecutor Randy M. Mastro, a deputy mayor under Rudy Giuliani, said Burress' case was going to be "a close call."
"He's got a pretty compelling story to tell," Mastro said. "But, at the same time, there's been a tremendous public outcry, particularly by some politicians, about this famous figure having a weapon."
Mayor Michael Bloomberg, who has waged a long campaign against illegal guns, has publicly castigated Burress for carrying the .40-caliber weapon. And there was talk of a cover-up by the Giants and the NFL after the Nov. 28 incident at the Latin Quarter after it took police nearly 12 hours to figure out Burress had shot himself and was hospitalized; the player turned himself in three days later.
Bloomberg's office on Monday said the mayor will leave it to prosecutors to decide how to handle the case.
Burress' Giants teammates have been supportive about his return. The Giants lost four of their final five games after Burress was suspended, fined and placed on the non-football injury list, meaning he also could not appear in the playoffs.
The Giants finished 12-5, losing at home in the playoffs to the Philadelphia Eagles.
The Giants, who signed Burress to a five-year, $35 million contract extension in September, have left the door open for his return once his legal issues are resolved.
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Associated Press Writer Colleen Long and AP Sports Writer Tom Canavan contributed to this report.
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