But the decision offered no guarantees that the journalists, who have been imprisoned for more than a year and now face a potentially lengthy second trial, would be freed anytime soon.
The convictions of the three men, Mohamed Fahmy, Baher Mohamed and Peter Greste, focused international condemnation on the government, drawing attention to a sweeping crackdown on news media freedom and political dissent since the military ouster of the country’s first democratically elected president, Mohamed Morsi of the Muslim Brotherhood.
And from its beginnings, analysts say, the case has perhaps had little to do with the actions of the journalists themselves. Instead, they suggest it reflects a bitter dispute between Egypt’s military-backed government, led by President Abdel Fattah el-Sisi, and Qatar, which owns Al Jazeera and has been a strong backer of his Islamist opponents in the Muslim Brotherhood.
The men were convicted in June on charges that included conspiring with the Muslim Brotherhood to broadcast false reports, though prosecutors presented no evidence for such claims. All three were sentenced to seven-year prison terms, but Mr. Mohamed received three additional years for possessing a spent bullet casing that he picked up at an anti-government street protest.
The case has drawn special notice partly because the defendants had reputations as experienced journalists and had in the past worked for other well-known international news organizations. But their ordeal, which the men have outlined in letters from prison and in messages sent through family members, has also highlighted the plight of thousands of Egyptians — including Islamists, leftist activists and other journalists — swept up by the authorities on charges that are widely viewed as politically motivated.
As the families of the Al Jazeera journalists sifted through the meaning of the latest court decision on Thursday, they applauded the court’s apparent criticism of the first trial but expressed disappointment that the judges had not granted a request to suspend the men’s sentences.
“We’ve learned not to expect anything,” said Mr. Greste’s father, Juris Greste. “We did expect a little better than this.”
Amal Clooney, a lawyer for Mr. Fahmy, noting what she said were numerous irregularities with the first trial, said her client could not rely solely “on the Egyptian judicial system to give us a necessarily fair or speedy outcome.”
In addition to focusing on the court proceedings Mr. Fahmy’s legal team was “doubling its efforts on the political and diplomatic tracks,” she said. “That seems to be the most promising way to achieve the outcome that is just.”
Mr. Sisi has said that the journalists should have been deported rather than stand trial, but he has so far insisted that the government does not interfere in judicial decisions.
A recent thaw in relations between Egypt and Qatar, brokered by Saudi Arabia, has raised hopes that the Egyptian president might be more willing to free the men. In December, in a major concession, Qatar suspended the broadcast of an Egyptian affiliate of Al Jazeera that had been sharply critical of Egypt’s government.
But the Qatari government has also refused to extradite Brotherhood leaders and supporters wanted by the Egyptian government, a source of continuing tension, according to Egyptian officials.
Although the appeals court did not give specifics for its decision, it is regarded as among Egypt’s most rigorous and independent legal bodies and may have been eager to remove the stain on Egypt’s judiciary after the spectacle of the first trial.
It was unclear whether the ruling made it any more likely that Mr. Sisi would step in before or during the retrial. The delay of a final decision could be useful in diplomacy with Qatar, or it could be viewed as an obstacle if Egyptian officials were quickly trying to rid themselves of a public-relations headache.
Mr. Sisi had issued a decree in November allowing him to deport non-Egyptians convicted of crimes, in an apparent sign that his government was seeking face-saving ways to end what has been an embarrassing case.
The decree could free Mr. Fahmy, who holds Canadian and Egyptian citizenship and Mr. Greste, an Australian, but it would not help Mr. Mohamed, an Egyptian citizen.
Ms. Clooney said that Mr. Sisi could act in several ways to free the journalists, including by granting a pardon at any time, releasing them on humanitarian grounds, or deporting Mr. Greste and Mr. Fahmy. “There is no reason this can’t happen quickly, and today’s decision doesn’t change that,” she added.
In their request for a new trial, lawyers argued that the previous case had had procedural errors, including that a “special court” had been illegally designated to hear the case, according to Negad el-Borai, another lawyer for Mr. Fahmy. The prosecutor also requested a new trial, Mr. Borai said, though the reasons have not been made public.
The defendants were not present Thursday, and reporters were barred from entering the court until after the hearing. Relatives of the men spoke to reporters after the decision and seemed stunned that they would not be released.
“I don’t know what the next step is,” said Marwa Omara, Mr. Fahmy’s fiancée. “It seems like it’s a long battle.” She added that Canadian officials needed to “do more.”
Lawyers said Thursday that the three journalists could still be granted bail at the start of their new trial, which is expected to begin within a month.
In a statement after the court decision, Al Jazeera said that the Egyptian authorities had a choice: “Free these men quickly, or continue to string this out, all the while continuing this injustice and harming the image of their own country in the eyes of the world. They should choose the former.”