The decision by the fundamentalist Islamic group, which has been outlawed since 1954 but fields candidates as independents, comes as Egypt's leadership seeks to defuse mass demonstrations - now in their 13th day - by proposing reforms but stopping short of the protesters' key demand that Mubarak step down.
The talks would be the first known discussions between the government and the Brotherhood in years - marking a startling shift in policy after years of crackdowns by the Western-backed regime against the Islamists. It also raised the possibility the group could be on its way to official recognition of its key role in Egyptian society.
The Brotherhood said in a statement that its representatives would meet with Vice President Omar Suleiman to press its "legitimate and just demands." Suleiman has accused the Brotherhood, businessmen and foreigners he did not identify as being behind a wave of looting and arson that swept much of the country last weekend after security forces inexplicably withdrew from the streets.
Meanwhile, a sense of normalcy began to return to the capital of some 18 million people, which has been largely closed since chaos erupted shortly after the protests began on Jan. 25.
The government opened a limited number of banks for the first time in a week, although just for three hours. Long lines formed outside banks in Cairo's downtown area and in the wealthy neighborhood of Zamalek.
Also in Zamalek, home to many foreign embassies, several food outlets opened for the first time since Jan. 25. Pizza delivery boys checked their motorbikes. Employees at a KFC restaurant wiped down tables. Hairdressers and beauty salons called their patrons to let them know they were reopening.
Traffic also was back to near regular levels and more stores reopened across Cairo, including some on the streets leading to the central Tahrir Square - signals many hoped would ease enormous economic losses. Protesters greeted some store owners with flowers.
Negotiations with the opposition reflect the regime's apparent determination to end the crisis by placating protesters with reforms but keeping Mubarak in office until elections can be held as scheduled in September. The United States shifted signals and gave key backing to the regime's gradual changes on Saturday, warning of the dangers if Mubarak goes too quickly.
Mubarak has promised not to run again but insists on serving out the remainder of his term to supervise a peaceful transfer of power. He also has vowed to introduce political reforms and to fight corruption - promises he has made several times over the decades of his rule.
Leaders of Mubarak's ruling National Democratic Party, including his son Gamal and longtime aides, resigned on Saturday.
Suleiman, a former chief of intelligence and army general, said Gamal, a 47-year-old banker-turned-politician, would not run for president, addressing longtime fears that he was being groomed for the post.
But the concessions so far have failed to satisfy the protesters, who insist that Mubarak immediately leave office.
"We are determined to press on until our number one demand is met," said Khaled Abdul-Hameed, a representative of the protesters.
He said the protesters at Tahrir Square have formed a 10-member "Coalition of the Youths of Egypt's Revolution," including a Brotherhood representative, to relay their positions to politicians and public figures negotiating with the regime. "The regime is retreating. It is making more concessions everyday," Abdul-Hameed said.
About 5,000 protesters filled Tahrir Square Sunday afternoon.
Mubarak, Egypt's iron-fisted ruler of nearly 30 years, is known to have little or no tolerance for Islamist groups and the decision to open talks with the Brotherhood is a tacit recognition by his regime of their key role in the ongoing protests as well as their wide popular base.
Suleiman and Prime Minister Ahmed Shafiq have rejected calls for Mubarak's immediate ouster, arguing that demanding his departure was a betrayal of the services he offered the country both as a career air force officer and president.
Senior Brotherhood leader Mohammed Mursi told The Associated Press the group was sticking to the protesters' main condition that Mubarak step down. He also rejected proposals that Suleiman take over from Mubarak on an interim basis to oversee reforms. It is not clear whether Egypt's constitution allows the vice president to assume any of the president's duties while he is still serving in office.
The Brotherhood aims to create an Islamic state in Egypt, but insists that it would not force women to cover up in public in line with Islam's teachings and would not rescind Egypt's 1979 peace treaty with Israel.
The group, which fields candidates as independents, made a surprisingly strong showing in elections in 2005, winning 20 percent of parliament's seats. However, thousands of its members were arrested in crackdowns over the past decade and it failed to win a single seat in elections held late last year. The vote was heavily marred by fraud that allowed the National Democratic Party to win all but a small number of the chamber's 518 seats.
Some opposition leaders met with Suleiman on Saturday but said there was no breakthrough.
At the focal point of the protests, Tahrir Square in central Cairo, some protesters said they had slept under army tanks ringing the plaza because of fears they would be pulled out overnight as part of a plan to evict them.
Hundreds at the square performed the noon prayers and later offered a prayer for the souls of protesters killed in clashes with security forces.