Hernandez was in court for what was supposed to be a probable cause hearing, but prosecutors said they are still presenting evidence and the grand jury is still considering it.
Judge Daniel O'Shea rescheduled the probable cause hearing for Aug. 22.
Hernandez has pleaded not guilty to murder in the death of Odin Lloyd, a 27-year-old Boston semiprofessional football player whose body was found June 17 in an industrial park near Hernandez's home. He had been shot five times.
Bristol County assistant district attorney William McCauley said additional evidence includes boxes of ammunition found at a condominium Hernandez leased and a magazine clip for a .45-caliber Glock in a Hummer registered to him. Police say Lloyd was killed with a .45-caliber gun. McCauley said the box had Hernandez's fingerprints on it.
Hernandez's attorney James Sultan objected to the delay, saying his client already has been jailed for four weeks and that the district attorney could have waited to bring charges but chose to go ahead last month.
"He made it sound like a slam-dunk case," Sultan said.
As Hernandez appeared for the hearing, detectives on the case approached a female cousin of Hernandez in court and seized her cellphone, ABC News has learned. That cousin, Tanya Singleton, shared a home with Ernest Wallace, who is charged as an accomplice in Lloyd's murder.
Investigators plan to execute a search warrant at Singleton's Bristol, Conn., address on Wednesday night, several sources told ABC News.
Singleton's husband, Thaddeus "TL" Singleton III, 33, was being sought for questioning as a potential witness in connection with the Hernadez case, but he was killed in a single-car crash in Connecticut before detectives could speak with him. The car in that crash was registered to Tanya's father, Hernandez's uncle, Andres Valderrama.
Outside court, another of Hernandez's attorneys, Charles Rankin, said he was "extremely disappointed" that prosecutors weren't prepared to go forward and that he's confident Hernandez will be exonerated.
Hernandez's girlfriend, Shayanna Jenkins, was in court for the hearing -- Hernandez mouthed "I love you" in her direction before he was led out -- but she did not respond to reporters' questions as she left the courthouse.
Members of Lloyd's family also attended the hearing but did not comment.
Also Wednesday, O'Shea ruled in favor of media organizations, including The Associated Press, that were seeking access to more documents in the case, including two arrest warrants, additional search warrants and other materials. The records will be released at 3 p.m. Thursday if no one appeals.
Two alleged accomplices in the Lloyd case, Carlos Ortiz and Wallace, also are in police custody.
Meanwhile, a judge unsealed three of four Connecticut search warrants from the investigation into Lloyd's death. The warrants were used to search Hernandez's uncle's home, an apartment and a rental car police say was used by Wallace and Ortiz the day after the shooting.
The items seized from the home last month include Correction Department documents linked to Ortiz and Wallace, a plastic gun box and two boxes of .38-caliber ammunition.
Bristol police also have been investigating a possible link to a 2012 fatal shooting in Boston and earlier said they had seized an SUV wanted in that investigation from the uncle's home.
With a Suffolk County grand jury probing the shooting deaths of two Cape Verdean immigrants in their car in Boston on July 16, 2012, a law enforcement official told The Boston Globe on Monday, "The case against Hernandez appears to be strengthening."
Boston police made a possible connection between Hernandez and the double homicide after he came under scrutiny in the June 17 killing of Lloyd.
Information from The Associated Press was used in this report.