|Egypt's PM says stability returning, though protesters continue to demand president's resignation [Al Jazeera]
Egypt's Muslim Brotherhood has held talks with the government aimed at ending the country's political crisis.
As pro-democracy protests entered the 13th day on Sunday, the opposition group met with Omar Suleiman, Egypt's vice president, to press its "legitimate and just demands''.
Mohammed Mursi, a senior Brotherhood leader, said the group is sticking to the protesters' main condition that President Hosni Mubarak step down.
"We have decided to engage in a round of dialogue to ascertain the seriousness of officials towards the demands of the people and their willingness to respond to them," a Brotherhood spokesman said.
Attendees said participants included members of secular opposition parties, independent legal experts and business tycoon Naguib Sawiris. A representative of opposition figure Mohamed El Baradei was also in attendance.
Egyptian state television said Suleiman began meetings with prominent independent and mainstream opposition figures on Saturday to go through the options, which centre on how to ensure free and fair presidential elections while sticking to the constitution.
The proposal being promoted by a group of Egyptians calling itself the "The Council of Wise Men" involves Suleiman assuming presidential powers for an interim period pending elections.
But some opposition figures argue that would mean the next presidential election would be held under the same unfair conditions as in previous years. They want to first form a new parliament to change the constitution to pave the way for a presidential vote that is democratic.
An Al Jazeera's correspondent in Cairo said the Brotherhood joining the talks is "highly significant".
"They are interested in talking about the resignation of president Mubarak," he said. "They want parliament resolved, they want those responsible for violence of the last few days put on trial ... and wanting to be able to peacefully protest."
Al Jazeera's correspondent in Alexandria, one of the Muslim Brotherhood's strongholds, says many people are surprised by the group's decision to enter talks.
He said it's a major concession that might be seen as a "weakness" that the Brotherhood didn't hold on to it's previous statement that it wouldn't join negotiations until Mubarak resigns.
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The president on Tuesday said he would not seek re-election in September.
However, Cherif Bassiouni, president of the Egyptian American Society and a former UN human rights expert, said the Muslim Brotherhood has already proved itself to be a responsible participant in Egypt's legislative process.
"They participated in the 2005 legislative elections. They elected 88 members to the parliament. So they've had a role in the secular parliament."
Protesters in Cairo's Tahrir Square and in many Egyptian cities are staging a march on Sunday to commemorate what they described as "Day of Martyrs".
Muslims will also hold a prayer for victims of the uprising, protesters said.
The renewed demonstrations come as the government aimed to get people back to work with banks and businesses reopening, in the first clear test of how far protesters can keep up the momentum to topple the government.
Al Jazeera's correspondent in the capital said the scene in Tahrir was relatively calm shortly before dawn on Sunday in what has become a "tent city".
"It's generally been a quiet day, though there have been sporadic moments of excitement amongst the protesters. At one moment the army was placed in between two groups who were chanting rival slogans at each other.
"But it's relatively peaceful now, and they're hunkered in and around what has become an enormous tent city.".
The news of the Muslim Brotherhood joining the talks came as protesters vowed not to back down in their demand for Mubarak to step down and end his nearly 30-year-rule.
"They are steadfast and very sure in their aims and refuse to move," our correspondent in Cairo said. "But certainly we haven't seen the massive numbers that we've seen before."
"We have to be steady to topple the government," Ahmed Abdel Moneim, a 22-year-old student who has been sleeping in the square for days, said.
"The French Revolution took a very long time so the people could eventually get their rights. ... If we have to spend our life to get rid of Mubarak, we will."
Despite the demonstrations, the Egyptian president has remained defiant, refusing to step down immediately, as per the protesters' demands.
However, the leadership of Mubarak's ruling National Democratic Party (NDP) resigned en masse on Saturday, according to state television.
Hossam Badrawi has been appointed the new secretary-general of the party, replacing Safwat El-Sherif, a Mubarak loyalist, in that post. Badrawi, seen by many as a liberal voice in the NDP, will also replace Gamal Mubarak, Hosni Mubarak's son, as head of the party's policies bureau.
Other new appointees include: Dr Mohamed Ragah Ahmed, Dr Mohamed Ahmed Abd El-Illah, Maged Mahmoud Younes El-Shirbiny, Mohamed Ahmed Abd El-Salam Hebah and Dr Mohamed Mostafa Kamal, according to an NDP press release.
Officials in the administration of Barack Obama, the US president, welcomed the resignation of Gamal Mubarak, terming it a "positive" move.
But the administration has continued to insist upon an orderly and peaceful transition in Egypt.
Frank Wisner, who has acted as an envoy for Obama by carrying a message to Mubarak, said on Saturday that the Egyptian president "must stay in office to steer" a process of gathering "national consensus around the preconditions" for the way forward.
PJ Crowley, the US state department's spokesman, has said, however, that Wisner was speaking as a private citizen, and that his views did not represent those of the US government.