In one street off the iconic square, focal point of the 2011 revolution, dozens of youths threw rocks over a cement wall erected by security forces as police responded with tear gas, AFP journalists said.[break]
In the square itself, thousands of protesters chanted slogans against the powerful Muslim Brotherhood from which President Mohamed Morsi hails.
His opponents accuse Morsi, the country´s first freely elected president, of failing to reform post-revolution Egypt while consolidating power in Brotherhood hands.
"The people want the downfall of the regime!" they chanted.
"Lift your head up high -- you are not a Muslim Brother," others said, echoing a signature chant of the uprising telling Egyptians to be proud.
"The performance of Morsi and his government is not good enough. If we give him the opportunity, the country will face ruin," said shop assistant Mostafa Abdallah, 23.
The opposition has called for mass protests on Friday against both Morsi and the Brotherhood, under the same slogan that brought Egypt to its feet in 2011: "Bread, freedom, social justice."
"Egypt needs a new revolution for the youth and for real democracy," said Ahmed Shawky, 65.
Marches from several parts of the capital headed for Tahrir Square, with protesters carrying huge Egyptian flags in scenes reminiscent of the 2011 protests.
Rallies were also staged in dozens of other cities and towns, organisers and officials said.
"Go out into the squares to finally achieve the objectives of the revolution," opposition leader and former head of the UN nuclear watchdog Mohamed ElBaradei wrote on his Twitter account.
"May God keep the country safe" read the headline of the independent daily Al-Shorouk, as the state-owned Al-Gomhuria pleaded for calm by urging people to "side with the nation."
The Muslim Brotherhood has not officially called its own rallies, instead marking the second anniversary by launching a charitable and social initiative dubbed "Together we will build Egypt."
On Thursday, police clashed with protesters who tried to dismantle the concrete barrier.
Some demonstrators hurled rocks at riot police who responded with tear gas. The interior ministry said five policemen were injured and appealed to demonstrators to avoid confrontation.
Morsi urged Egyptians to spend the anniversary in a "peaceful and civilised way," in a Thursday speech marking the Prophet Mohammed´s birthday.
But the threat of violence remained, especially with a court verdict due on Saturday in the trial of dozens of defendants over the worst football disaster in Egyptian history.
More than 70 people were killed in Port Said last February during clashes in the Suez Canal city between fans of home side Al-Masry and diehard supporters of Cairo´s Al-Ahly, known as Ultras.
Al-Ahly supporters warned of violent protests and a "new revolution" if Saturday´s verdict goes against them.
After the seismic political changes of 2011, the Arab world´s most populous nation is struggling to find a balance between a leadership that boasts the legitimacy of the ballot box and opponents who accuse the Islamists of betraying the goals of the revolution that brought them to power.
Egypt is also in the throes of an economic crisis as foreign investment and tourism revenues dwindle, the Egyptian pound stands at its lowest level against the dollar and a budget deficit shows no sign of recovery.
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