(CNN)-- Egypt's first ever democratically elected president, Mohamed Morsi, will make history in another way: by appointing a woman as vice president, his policy adviser told CNN.
He will also choose another vice president who is Christian, Ahmed Deif said.
The news came as the man Morsi beat for the presidency, Ahmed Shafik, left Egypt on a trip to Abu Dhabi, and as Cairo's administrative court overturned a rule that allowed the military to arrest people without a warrant.
"For the first time in Egyptian history -- not just modern but in all Egyptian history -- a woman will take that position," Deif told CNN's Christiane Amanpour on Monday, referring to one of the vice presidency slots. "And it's not just a vice president who will represent a certain agenda and sect, but a vice president who is powerful and empowered, and will be taking care of critical advising within the presidential Cabinet."
Although Morsi has previously argued for banning women from the presidency, he said before the election that as president he would stand for women's rights.
"The role of women in Egyptian society is clear," Morsi told Amanpour through a translator weeks before the runoff election. "Women's rights are equal to men. Women have complete rights, just like men. There shouldn't be any kind of distinction between Egyptians except that is based on the constitution and the law."
The Islamist figure, a Muslim Brotherhood leader, also promised to ensure rights of minorities.
Egypt "definitely" will not be an "Islamic Republic," Deif said Monday.
Morsi moved into his offices Monday, said Jihad Haddad, an adviser to the transition team.
He began the work of assembling a new government -- one of the tasks he maintains the power to do after the military junta running the country recently slashed the presidency's reach.
The process of picking people to serve in the Cabinet will take time and "won't end in a day," Haddad said.
Shafik, who lost in the runoff election to Morsi, left the country Tuesday for the United Arab Emirates, his attorney and a Cairo airport official said.
He traveled to Abu Dhabi, Cairo airport official Mohamed Sultan said.
He is not fleeing the country, Shafik's attorney, Showee Elsayed, told CNN.
While some legal petitions accusing Shafik of corruption were submitted in April, prosecutors have not taken legal action on them, so "there are absolutely no legal cases pending against" him, Elsayed said.
Shafik was the final prime minister to serve under ousted President Hosni Mubarak.
Shafik's office said Tuesday he "will establish a new political party upon his return from the UAE and Saudi Arabia where he is on private visits."
He and his two daughters will be performing Umra, an Islamic religious pilgrimage to Mecca.
Meanwhile, Cairo's administrative court, which hears civilian complaints against the government, rejected a controversial rule Tuesday that the ministry of justice had established before the election.
The rule stated that military personnel and intelligence forces could arrest civilians without a warrant.
Fourteen legal complaints were filed about the rule by various people and groups, including the Muslim Brotherhood.
The right to arrest civilians was previously reserved for police officers, the state-run Ahram news agency reported.