Egypt's prime minister-designate is to offer ministerial posts in the new government to members of the Freedom and Justice Party, the Muslim Brotherhood's political arm, and to the hardline Islamist Nour Party.
"There is no objection at all to including members of those two parties in the government," state news agency MENA quoted a presidential spokesman as saying.
Meanwhilke, Egypt's interim president has named liberal economist and former finance minister Hazem el-Beblawi as prime minister in a transitional government.
Acting head of state Adli Mansour also appointed former UN nuclear agency chief Mohamed ElBaradei as deputy to the president, responsible for foreign affairs.
The Nour Party, which has held up the political process by objecting to several candidates put forward by military-backed interim authorities, said it would support Mr Beblawi's appointment.
The head of the party added that it was still studying Mr ElBaradei's appointment.
The Muslim Brotherhood has rejected a decree issued by Egypt's interim head of state overnight, which set a timetable for new elections and set up a mechanism to amend the constitution.
Senior Brotherhood politician Essam El-Erian said the decree by Mr Mansour was "usurping legislative power" and an act of "someone appointed by the putschists".
Mr Mansour's decree sets out a timetable that could lead to parliamentary elections in about six months, to be followed by a new presidential election.
The constitution would be amended and again put to public vote in a referendum.
The Brotherhood is demanding the military reinstate Mr Mursi as president and has said it will have nothing to do with the military-backed transition.
Mr Mursi's supporters have called for further protests.
At least 51 people were killed yesterday when the army opened fire on Mursi supporters who were camped outside Cairo's Republican Guard barracks.
The military said it opened fire in response to an attack by armed assailants.
On Friday, clashes between pro- and anti-Mursi supporters swept Egypt and left 35 dead.
The Muslim Brotherhood movement called for more protests today, raising the risk of further violence.
However, an umbrella group representing anti-Mursi protesters said they would not demonstrate.