Amal Clooney and Mark Wassouf of British firm Doughty Street Chambers said in a statement that Mohammed Fahmy is in prison for over 300 days on the basis of a "fundamentally unfair" trial.
Fahmy, Australian Peter Greste, and Egyptian Baher Mohammed were charged with helping the Muslim Brotherhood, a group Egypt's government has declared a terrorist organization. Fahmy and Greste were sentenced in June to seven years and Mohammed to ten in a trial described as a sham.
In a sign that the case, which has caused an international outcry, may be coming to a close, President Abdel-Fattah el-Sissi said last week that he is examining ways to resolve the matter.
El-Sissi was responding to a question about whether he considered issuing a pardon for the defendants or deporting the foreign defendants in the case.
The law passed this month was seen as providing a potential legal instrument with which to free the journalists.
The attorneys welcomed el-Sissi's statement. They said a pardon would be in line with a regional reconciliation agreement reached this month that sought to end tension between Qatar, Egypt and other Gulf countries over Doha's support for Islamist groups, including the Brotherhood.
The attorneys called on Al-Jazeera and Qatar to respect the agreement, "which requires that parties should not foment hatred between groups but rather work openly and co-operatively with each other in a spirit of reconciliation."
The lawyers also called on the country's chief prosecutor to release Fahmy, who suffers from Hepatitis C and an injured shoulder, because the ailments require urgent treatment.
The Al-Jazeera journalists' arrest last December was part of a broad crackdown against Islamists in which hundreds have been killed and thousands arrested. The journalists say they are being prosecuted simply for doing their job.
Fahmy, who covered stories for the New York Times and CNN before working for Al-Jazeera, was the most outspoken over the course of the trial.
His family, who moved to Canada in 1991, has called the charges against the three journalists "ridiculous."
Canadian officials have told Fahmy's family that the journalist's dual citizenship has placed limits on how much they can do.
The trio appealed their sentences and a court has set an appeals hearing for Jan. 1, 2015.
_ With files from The Canadian Press.
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