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The sister of jailed Egyptian dissident Alaa Abdel Fattah attended the protest but did not address the media or the onlooking crowd.
Sanaa Abdel Fattah said on Thursday that a lawyer for Abdel Fattah was still seeking access to visit him at a prison north of Cairo and negotiations were ongoing.
Many of the protest chants played on the title of her brother’s recently published book, You Have Not Yet Been Defeated.
The relatively small protest came hours before Abdel Fattah's lawyer said Egypt's state prosecutor had granted permission for him to visit the activist.
On Thursday afternoon, he said he was negotiating access with prison authorities.
Egypt has largely banned protests for much of the past decade.
Allowing the protest to proceed honoured Egypt’s repeated pledges to allow peaceful protests at the UN summit.
The protest took place at a time when Egypt has come under growing Western diplomatic pressure to free Abdel Fattah.
Abdel Fattah, 40, a well-known figure from the 2011 uprising that forced long-time president Hosni Mubarak to step down, began a partial hunger strike in April.
He declined liquids on Sunday, according to his family, who warn he could die.
Late on Thursday, Egypt's general prosecution said a thorough medical examination of Abdel Fattah, including blood tests, showed that he was in good health and did not need to be transferred to hospital.
"This suggests that it's doubtful that he is on a hunger strike," it said.
Thursday’s protesters held banners in English, French, Arabic and Spanish saying: “No climate justice without human rights.”
Most protesters wore white clothes and face coverings. They raised their fists as they chanted: “The people united will never be defeated.”
“We are here to raise the voices of all the climate and human rights defenders,” prominent Colombian activist Gina Cortes Valderrama told the crowd.
“We cannot forget those many, many, many who lost their voices,” said Ms Valderrama, the first of eight speakers to address the rally.
Sanaa Abdel Fattah, has been speaking about her brother’s case since she arrived this week in Sharm El Sheikh, the Red Sea resort where the UN meeting is held.
Abdel Fattah and siblings Sanaa and Mona became British citizens this year because their mother, mathematics professor Laila Soueif, was born in the UK.
In the past few days, the leaders of France, Britain and Germany said they discussed his case with Egyptian President Abdel Fattah El Sisi in Sharm El Sheikh and called for his release.
Abdel Fattah is serving a five-year prison sentence for "spreading false news" based on a Facebook post.
When asked about Abdel Fattah, Egyptian Foreign Minister Sameh Shoukry said this week that the dissident was treated in accordance with prison regulations and the penal code.
Abdel Fattah, he said, has access to “all the necessary care in prison."
On Wednesday, the minister said that raising the dissident’s case during the UN summit was designed to distract from the “organisational achievement” made by Egypt as host.
Mr El Sisi, who took office in 2014, has partially eased policies regarding dissent in recent months.
He has approved the release of about a 1,000 government critics who had been in pre-trial detention and called for the convening of a national dialogue on the country’s political future.
He has also allowed carefully measured criticism of his policies at a time when his country’s economy has been affected by the fallout from the Russia-Ukraine war.
The head of Egypt's National Council for Human Rights whose members are appointed by parliament, said on Wednesday she hoped for a positive outcome to Abdel Fattah's case and others.
"We want really to see no one deprived of his liberty because of an opinion he or she expressed," Moushira Khattab, NCHR President said. "But we want everyone to get the same chance."
But one pro-government TV talk show host, Ahmed Musa, spoke about an international conspiracy to destabilise Egypt.
“No one can rattle Egypt. It’s a powerful nation and you need to realise that,” he said, addressing western leaders who called for Abdel Fattah’s release.