As a weak sign for the society back, slowly, to normal, the curfew time was shortened to 11 hours, from 7 p.m. (1700 GMT) to 6 a.m. (0400 GMT) compared to the previous 17 hours, from 3 p.m. ( 1300 GMT) to 8 a.m. (0600 GMT).
The United States, a close ally of Egypt, has called for an orderly transition of power in the unrest-hit country now. The White House on Friday urged the Egyptian government to take " concrete steps" toward an orderly transition of power and warned that without such measures there would be no peaceful resolution.
Mubarak, 82, said on Thursday he wanted to leave office but that he feared his resignation would bring chaos to Egypt.
Handing presidential powers to Vice President Omar Suleiman seems to some analysts a potential compromise between protesters' demands for Mubarak to resign now and his decision to finish the rest of his term until September.
Suleiman, 74, Egypt's former intelligence chief, was appointed last week to be the first-ever vice president in the recent 30 years. He served as the country's intelligence chief and took charge of Egypt's most vital political files.
As a move to please the opposition, Suleiman announced on Thursday that Mubarak's son Gamal Mubarak, who now heads the policies committee of the ruling National Democratic Party (NDP), will not seek presidency in the upcoming polls in August or September.
Prominent figures that have the prospect to run for presidency include Amr Moussa, secretary general of the Arab League, and opposition leader Mohammed ElBaradei.
Amr Moussa, also Egypt's former Foreign Minister, said he believed Mubarak would hold on until September's election. Regarded by some as a possible successor to Mubarak, Moussa told France's Europe 1 radio Friday that he would consider standing. He visited the Tahrir Square to meet protestors on Friday.
ElBaradei, 68, a retired chief of the International Atomic Energy Agency (IAEA), has repeated he was ready for a role in helping Egypt achieve political change if Mubarak resigned now.
In a phone interview with Al Jazeera on Friday, ElBaradei said: "if the Egyptian people want me to continue the change process, I will not disappoint the Egyptian people."