Egypt's new prime minister, Essam Sharaf, has pledged to meet the demands for democratic change sought by protesters, and to resign if he fails.
He made the comments in an address before thousands gathered at Cairo's Tahrir Square before Friday prayers.
The former transport minister told the crowds that he drew his "will and determination" from the people.
Mr Sharaf has replaced Ahmed Shafiq, who was appointed in the dying days of the regime of Hosni Mubarak.
He was named as head of the transitional caretaker government by the army on Thursday.
A US-educated civil engineer, he opposed Mr Mubarak's government after stepping down from the cabinet five years ago. He actively supported the revolution, joining the street protests in the capital.
He was carried to and from the podium on the shoulders of protesters but declined the crowd's pleas to take the oath of office in front of them and left the square to chants of "Take the oath, take the oath, take the oath".
The protesters had planned Friday's rally to call for the resignation of Mr Shafiq but went ahead with the gathering as a celebration of the appointment of Mr Sharaf.
On Friday, it was announced that a referendum on constitutional reform in the country would be held on 19 March. Elections for parliament and to choose a new president are scheduled within six months.
Mr Mubarak is believed to be living in his villa in Sharm el-Sheikh, but is in poor health, and has not been seen or heard of publicly since stepping down.