President Mohamed Morsi infuriated many last Monday with his appointment of Adel Mohamed Al-Khayat, reaching out for a political alliance with the more radical al-Gamaa al-Islamiya ahead of a big wave of opposition-led protests expected to start on June 30.
But Al-Gamaa Al-Islamiya, which has renounced violence, appeared to want to show that it could put Egypt's needs first - especially the tourist industry, a mainstay of the economy that has suffered badly in two years of unrest.
Safwat Abdel Ghani, one of the group's leaders, was quoted by Al-Ahram news website as saying the governor would announce his resignation on Sunday. Sources in the cabinet and the presidency said they were not aware of such move.
"We are not after any post," Abdel Ghani told an earlier news conference. "We asked the new governor to resign for the sake of Egypt."
Both Morsi's Islamists and the leftist-secular opposition are trying to marshal support before June 30.
On Friday, thousands of protesters from al-Gamaa al-Islamiya, the Muslim Brotherhood and other Islamist groups staged a big pro-Mursi rally and warned opponents, who they described as atheists, Western agents and anti-Islamic, that they would be crushed if they forced Mursi out. The opposition called it an attempt to "terrorise" them.
Morsi's appointment of a large number of Islamist governors including Khayat triggered protests in many cities.
Mursi himself defended the appointment of Khayat in the newspaper Akhbar Al-Youm on Saturday, saying there had "never been a court ruling" against him, and cautioned that the state would act if the June 30 rally turned violent.
The protest is being organised by a group of young independent Egyptians called Tamarod (Rebel), which says it has gathered over 15 million signatures in a month - more than one in six of the population - calling for Mursi to quit.
Both the youth movement and established opposition leaders are demanding an early presidential election after what they describe as Mursi's failure to live up to any of his promises of more freedoms and better economic and living conditions.
But Mursi's allies say he needs more than a year in office to tackle Egypt's deep economic and political problems.
Al-Gamaa al-Islamiya renounced violence and condemned al Qaeda in ideological U-turns a decade ago, and recently founded the Building and Development Party to expand its political presence.
Many of its members were jailed for decades under president Hosni Mubarak, who was toppled by mass protests more than two years ago. Mursi freed them last year, shortly after his election, with many moving into public life.
However, some of the recently freed members still defend their violent past. Assem Abdel Maged, convicted and jailed for his role in the killing of more than 100 policemen in one attack in the 90s and now leading a pro-Mursi campaign, said he had never regretted any of his actions.