Ibrahim Halawa, the son of the most senior Muslim cleric in the Republic of Ireland, was arrested during a siege on the Al-Fath mosque in Cairo in 2013.
The mass trial of Mr Halawa and 493 others began in March after being postponed five times since his arrest.
Mr Halawa, 19, could face the death penalty if he is convicted.
Mr Halawa was on a family holiday to his parents' homeland when he and three of his sisters were arrested by Egyptian security forces during a crackdown on protests in the country's capital.
He was 17 at the time.
His family said he had taken refuge in the building during violent clashes between supporters of ousted president Mohammed Morsi and the security forces.
His sisters were allowed to return to Dublin in November 2013.
On Wednesday, a hearing in his case took place, with Irish officials in attendance.
But it could not proceed as 16 defendants were not present in court, according to the Irish Department of Foreign Affairs.
Defence lawyers requested that the trial would not proceed during the forthcoming Ramadan period and the judge agreed to adjourn the matter until 2 August, the department added.
Amnesty International Ireland said Mr Halawa should be released immediately with all charges against him dropped.
Colm O'Gorman, the human rights organisation's executive director in Ireland, said the situation was "utterly unacceptable".
"No one should have to withstand the continual raising of hope that they might have their day in court, only to have that hope continually dashed," he said.
"This young man should be at home in Ireland, continuing his studies and getting on with his life."
He added: "I urge the Irish government and their EU partners to continue to work on Ibrahim's case as an absolute priority."

Australian of the Year and domestic violence campaigner Rosie Batty said on Thursday the "unsafe" camps must close.
Nearly 450 staff at Mr Turnbull's former university have also expressed concern about claims of torture by government employees and contractors.
Australia intercepts all irregular boat migrants and holds them in camps in Nauru and Papua New Guinea.
Mr Turnbull has defended the rules, a central policy of former Prime Minister Tony Abbott, by saying they are tough but save lives.
In a letter to Mr Turnbull, Ms Batty said those detained in offshore centres needed care, instead of punishment.
"The centres are, by their very design, unsafe and dangerous places. These centres cannot be patched up," she said.
The academics, meanwhile, said there was "overwhelming" evidence that "repugnant acts" including torture and abuse had been carried out the camps.
This week, the Australian Broadcasting Corp aired allegations made by a Somali woman who said she was raped by two men on Nauru - and that it took police on the Pacific island four hours to respond.
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Australia's controversial asylum policy
Mr Turnbull said the rape claims raised in the report were "very alarming", but defended the government's stance on border security.
"The one thing we know is these policies, tough though they are, harsh though they are in many respects, actually do work, they save lives," Mr Turnbull said.
"We're taking a number of steps to work closely with the Nauru government to ensure the safety and the security of all the refugees living in that community."

The 34ft (10m) catamaran crashed into the turbine off the coast of Cumbria, about 2.5-miles (4km) off Walney Island, near Barrow.
An RNLI lifeboat from Barrow rescued the crew and brought them to shore shortly after 02:50 BST.
One of the men, aged 58, suffered a head injury and was taken to hospital for treatment.
The fishing vessel had been travelling from Ravenglass at the time of the incident.
The RNLI towed the vessel back to shore.
The trial of a Dublin teenager held in an Egyptian prison for almost two years has been adjourned for a third time.
[NEXT_CONCEPT]
Australia's new PM Malcolm Turnbull is facing fresh calls to shut down offshore migrant detention centres.
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Three men have been rescued after their fishing boat collided with an offshore wind turbine and began to sink.