As the Army tried to clear the Square to enable the movement of traffic, scuffles broke out between the soldiers and some of the protesters who have chosen to stay put until further guarantees from the new leadership.
The military police chief has asked the area to be cleared today but many demonstrators are in no mood to return even after 20 days.
"We do not want any protesters to sit in the square after today," said Mohamed Ibrahim Moustafa Ali, the head of military police.
Though hundreds of protesters still remained in the Tahrir Square, life was inching towards normalcy as markets and businesses reopened and Egyptians went back to daily work on their first working day post the fall of Hosni Mubarak.
Egypt`s cabinet is to meet for the first time after Mubarak`s departure from power, as anxious Egyptians waited for more concrete announcements towards a transition from the caretaker government.
Protest organisers have already threatened more rallies if the Supreme Military Council, that is incharge of the government, fails to accept their agenda for reform.
"If the army does not fulfil our demands, our uprising and its measures will return stronger," a protest leader was quoted as saying by Al Jazeera.
The protesters have said they want the dissolution of the parliament and the lifting of a 30-year-old state of emergency.
The Egyptian military which took control of the administration after Mubarak stepped down has asked the people to get back to work to restore stability in the country, but many people are worried about the possibility of the movement squandering down with time.
Though the caretaker leadership has promised that it will lift the emergency and oversee a peaceful transition to democracy, it has not laid out any timetable for these steps.
"We do not want to leave because so much still needs to be done. They haven`t implemented anything yet," said a protester at the Tahrir Square.
The Egyptian cabinet, appointed when Mubarak was still in office, was meeting today for the first time after Mubarak bowed down to the public demand.
Its spokesman said that the cabinet will not undergo a major reshuffle but it will stay to oversee a political transformation in the coming months.
The Supreme Military Council had in a communique yesterday vowed to hand over power to an elected, civilian government in a peaceful transition.
According to the state television, prosecutors also opened an investigation into three former ministers of the Mubarak regime after the new government had imposed a travel ban on officials to make sure they do not flee.
Travel ban was imposed on the much-despised former information minister Anas el-Fekky, who resigned yesterday in the midst of accusation of waging a media campaign against the protesters.
Travel ban was also imposed on former prime minister Ahmed Nazif and former interior minister Habib al-Adli, who were both sacked by Mubarak before he stepped down.
Egypt was overcome by joy after Mubarak stepped down, bringing an end to his three-decade of iron fisted rule.
The initial euphoria has now made way for concerns about the country`s future and the process of democratisation.
However, despite the uncertainty, celebrations have refused to die down in the capital and other cities.