Australian Peter Greste, Canadian Mohamed Fahmy and Egyptian Baher Mohamed were jailed last year for "spreading false news" during their coverage of the turmoil after the army ousted Islamist president Mohamed Morsi in 2013.
Greste, who has since been deported, and Fahmy received seven years in the initial trial, while Mohamed was jailed for 10 years.
An appeals court ordered a retrial, saying the verdict lacked evidence against the three journalists working for the Doha-based network's English channel.
The ruling is now expected on August 2, state news agency MENA reported. Earlier some relatives and lawyers said it was set for August 8.
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"We are extremely angry that the verdict has been adjourned today," Al-Jazeera's English-language channel said on Twitter.
Today's session had been keenly awaited by rights groups and families of the defendants.
"The entire world has its eyes turned on Egypt because this is a decisive trial for media freedom," the Paris-based media watchdog Reporters Without Borders said Wednesday.
"It's disturbing that the trial was postponed without informing our lawyers," he told AFP outside the court.
"I don't want to predict anything about the verdict. Anything could happen."
An angry Fahmy said the delay was an insult to the defendants and their families.
"It was a very difficult week waiting for the verdict. I brought a bag with blue clothes and toothbrush, and now it's a more difficult week" ahead, he said.
"We have been in a nightmare for 19 months ... I see the postponement as another insult to us, our families, our lawyers because no one informed us officially."
Greste has already been deported under a law allowing the transfer of foreigners on trial to their home countries but he is being retried in absentia.
Fahmy and Mohamed were freed on bail earlier this year, having spent more than 400 days in detention.
Fahmy has renounced his Egyptian nationality, hoping that he too would be deported like Greste.
"If this trial is fair, me and my colleagues have to be acquitted," Fahmy told AFP on Wednesday, adding that a court committee had acknowledged that there had been "no fabrication" in their coverage.