President Mohamed Morsi’s opponents plan a rally, accusing the Islamist leader of betraying the revolution.
Mohamed Morsi denies the claim, and has called for “peaceful” celebrations.
An appeals court recently overturned Hosni Mubarak’s life sentence over the deaths of protesters and ordered a retrial.
The 84-year-old former leader remains in detention at a military hospital.
On Thursday evening, police clashed with protesters who tried to remove barriers blocking a road to Tahrir Square.
The clashes continued overnight, as police fired tear gas at demonstrators camping on the square. At least eight people were wounded, officials said.
Mohamed Morsi’s Muslim Brotherhood party has not officially called for its own street rallies. It plans to mark the revolution by launching charitable and social initiatives.
Protesters began converging on Tahrir Square on Friday morning.
One of them, Hanna Abu el-Ghar, said: “We are protesting against the fact that after two years of the revolution, where we asked for bread, freedom and social justice, none of our dreams have come true.”
The liberal opposition accuses Mohamed Morsi of being autocratic and driving through a new constitution that favors Islamists and does not sufficiently protect the rights of women or Christians.
Ahead of the planned rally Mohamed El Baradei, a leading opposition figure and former head of the UN atomic agency, said is a statement: “I call on everyone to take part and go out to every place in Egypt to show that the revolution must be completed.”
The government is also being blamed for a deepening economic crisis.
The president has dismissed the opposition’s claims as unfair, instead calling for a national dialogue.
Mohamed Morsi and his supporters accuse their opponents of undermining democracy by failing to respect the Islamists’ victory in elections a year ago.
In a speech on Thursday marking the Prophet Muhammad’s birthday, President Mohamed Morsi called on Egyptians to celebrate the anniversary “in a civilized, peaceful way that safeguards our nation, our institutions, our lives”.
Last month, Mohamed Morsi described the new constitution as “historic” and also said that boosting Egypt’s economy was his priority.
The president also admitted that mistakes had been made but insisted he would never make a decision except in the interests of the country.
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