The gathering in New York is being attended by both Prime Minister Stephen Harper and Egyptian President Abdel-Fattah el-Sissi — a rare coming-together Fahmy's family hopes might yield some results.
"It's an excellent opportunity to seize," Fahmy's brother, Adel Fahmy, told The Canadian Press. "I hope they can capitalize on it."
The family isn't necessarily hoping Harper will demand Mohamed Fahmy's immediate release — although that is their ultimate goal — rather, they hope Harper or his ministers can at least convince their Egyptian counterparts to move the case along.
"We (hope) that there will be a chance for the prime minister to speak to President el-Sissi about Mohamed and try to deliver the message that what we need is essentially two things — the appeal process to be expedited ... and also for the prime minister to ask that Mohamed get released for health reasons, a health release with bail and a travel ban," Fahmy's brother said.
Fahmy moved to Canada with his family in 1991, living in Montreal and Vancouver for years before eventually moving abroad for work, which included covering stories for the New York Times and CNN.
He was working for Qatar-based satellite news broadcaster Al-Jazeera English when he was arrested on Dec. 29 along with two colleagues — Australian correspondent Peter Greste and Baher Mohamed, an Egyptian producer.
The trio were accused of supporting the banned Islamist Muslim Brotherhood group of ousted Egyptian president Mohammed Morsi. They were also charged with fabricating footage to undermine Egypt's national security.
The journalists denied all charges, saying they were just doing their jobs.
After a trial which drew heavy international criticism, the trio were found guilty. Fahmy and Greste were sentenced to seven years in prison, while Mohamed was sentenced to 10 years.
Fahmy has since filed an appeal, but there hasn't been any movement on the file since August, his brother said, adding that any pressure from the Canadian government might help.
The family is supported in their call by the Canadian Journalists for Free Expression, which has written to Harper urging the prime minister to use his time at the UN General Assembly to demonstrate Canada's "commitment to human rights and democratic values on the international stage."
The request for Harper to address Fahmy's case comes as Egypt's president said this weekend that he can't interfere with his country's courts.
El-Sissi, who took power in June, said if he had been in power at the time Fahmy and his colleagues were arrested, he would have simply deported them instead of letting their case go to trial. But he said if Egypt is to have an independent judiciary, his government "can't accept criticism or comment'' on court rulings.
He did not, however, address whether he would pardon the three after their appeals process is finished.
While Fahmy's family accepts el-Sissi's remarks, they believe the Egyptian leader could still secure Fahmy's release on bail.
"We're just hoping that the president can give instructions to expedite the process. The appeal process in Egypt can be very long," Fahmy's brother said. "Mohamed's health is deteriorating and that's what alarms us the most."
Fahmy has hepatitis C, a condition his family has been hesitant to discuss but one which is an increasing source of concern.
Fahmy is also still dealing with constant pain from an injury to his right arm suffered shortly before his arrest. His family says his time in prison has meant the arm hasn't healed properly, leaving him with a "severe, chronic injury."
The family filed a request for Fahmy to be released on bail due to medical reasons in July, but are still waiting for it to be approved.
A request has also been filed with Egyptian authorities to allow Fahmy and his fiancee to be married while the journalist is still in prison, although that too hasn't been approved.
"It's a declaration of their love for each other and that Mohamed remains free behind bars," Fahmy's brother said. "It serves multiple purposes."
Meanwhile, Fahmy spends his days in a cell with his journalist colleagues trying to stay optimistic.
"There are good days and bad days but he's a strong character who shows strength and positivity," his brother said. "We cannot afford not to keep the hope, all of us."