An official from the Brotherhood, which the government has accused of trying to profit from the sweeping protests posing the greatest threat to Mubarak's three-decade grip on power, said talks would take place between the group and Egypt's new Vice President Omar Suleiman.
The official did not give a date for the talks, which will be the first ever between the government and its bete noire.
"Keeping in mind the interests of the nation and its institutions and concerned about preserving the country's independence... we decided to begin talks to see up to what point they are ready to accept the demands of the people," the official told AFP, speaking on condition of anonymity.
The official also said the dialogue was aimed at eliminating "foreign or regional interference in our affairs," in an effort to distance the group from Iran, which has called for the installation of an Islamist regime in Egypt.
The Brotherhood, which is officially banned but tolerated in Egypt, is the best-organised opposition movement drawing on a vast social aid network.
Senior members of Mubarak's party resigned on Saturday, but demonstrators staging a 12th day of anti-regime protests rejected the shuffle as a cosmetic move.
The resignations came after Mubarak huddled with his new government for the first time.
State television said the executive committee of the ruling National Democratic Party had resigned en masse. Among those stepping down was Mubarak's son Gamal, once viewed as his heir apparent. But protesters rejected it as a meaningless gesture.
"Some people say it is cleaning out but I believe these are cards they are throwing on the table to please the street, it's like a striptease show," said Mahmud Momen, a 46-year-old businessman.
Farid Ismail, a prominent member of the Muslim Brotherhood, said the resignations were a sign of the regime's demise.
"The regime's pillars are crumbling. This means that the revolution of the youth has caused a large earthquake and many of the regime's symbols are falling -- it is trying to save itself," he declared.
The political turmoil in Cairo loomed large over international meetings in Munich, Germany, where Obama's special envoy Frank Wisner said Mubarak should stay in office during a democratic transition.
"The President must stay in office in order to steer those changes through," Wisner, who met Mubarak this week, told the Munich Security Conference via video link, describing the leader as an "old friend" of the United States.
"President Mubarak's continued leadership is critical," he said.
But officials in Washington quickly distanced themselves from Wisner's remarks, saying he spoke as a private citizen.
US President Barack Obama spoke Saturday to several foreign leaders about the unrest in Egypt and underscored the need for "an orderly, peaceful transition, beginning now," the White House said in a statement.
The US leader spoke to Crown Prince Mohammed bin Zayed of the United Arab Emirates, Prime Minister David Cameron of Britain and Chancellor Angela Merkel of Germany, the statement said.
Cameron and Obama agreed that "real, visible and meaningful change needed to start now" in Egypt, a Downing Street spokesman said.
"The Prime Minister said that a clear and credible roadmap to change was needed as soon as possible, including a path to free and fair elections," the spokesman added.
At least 300 people are believed to have been killed and thousands injured since the protests began on January 25, according to the United Nations High Commissioner for Human Rights.
With big crowds swelling anew in Tahrir Square, Mubarak on Saturday met for the first time with the government he swore in five days earlier.
Present were his new Prime Minister Ahmed Shafiq, the ministers of petroleum, trade, finance and social solidarity, and the head of the central bank, official news agency MENA reported.