Rallies by the mainly secular opposition brought thousands of people on the streets, and violence was reported from several cities including Alexandria and Suez.
In the canal city of Ismailia, protesters set fire to the headquarters of the Muslim Brotherhood's Freedom and Justice Party (FJP).
In Cairo, tens of thousands of opposition supporters gathered at the Tahrir Square, the centre of the pro-democracy protests of 2011, with many chanting slogans denouncing the 'Brotherhoodisation' of the state.
Several marches started after Friday prayers from mosques to different parts of the city, with batches of protesters reaching the presidential palace as well as the state radio and television headquarters.
As protestors tried to storm the Egyptian radio and television building, the presidential guard used tear gas to disperse them.
Tear gas was also fired at protesters attempting to break a barricase outside the Ministry of Interior and outside the presidential palace, leaving as many as 120 injured.
Hardcore football fans known as 'Ultras' also joined the protests, storming underground stations in central Cairo and bringing the movement of trains to a halt.
They also stormed the internal radio station of the tube and chanted anti Muslim Brotherhood slohans.
Much has elapsed since the mass uprising of 2011 overthrew Mubarak, and Egyptians have for the first time elected a government of their own. But the developments have left the country sharply polarised.
The presidential vote that elected Brotherhood leader Mohamed Mursi as the president was far from overwhelming for any single candidate.
A recent referendum on the constitution also left the country deeply divided with the secular and liberal opposition terming the draft as "too Islamist" that would compromise on the rights of the minorities.
Not much has changed in the last three years in terms of anger at the economic and social polices and frustration towards achieving real changes.
The critics of Mursi say his policies side with the rich and are no different than those laws of Mubarak.
The division in Egyptian society was amply displayed today as thousands of protesters shouted slogans against the elected President and his government.
'Down with the rule of the (Muslim Brotherhood) Supreme Guide,' many chanted. 'The people demand the overthrow of the regime,' others said.
"Today the Egyptian people continue their revolution," said Hamdeen Sabahi, a leading opposition leader who finished a close third in the presidential elections held in June.
"They are saying 'no' to the Brotherhood state ... We want a democratic constitution, social justice, to bring back the rights of the martyrs and guarantees for fair elections," the socialist was quoted as saying by Al Ahram.
At least 25 people have been injured in clashes in Cairo since last night. Protests, sometimes violent, continued in Alexandria, Ismailia, Suez and Port Said.
In Alexandria, tear gas was fired at protesters.
Apprehending trouble, the Ministry of Interior posted a message on its Facebook page, asking protesters to express themselves but without violence.
"Dear revolutionaries, you have the right to protest, express your opinion as much as you want. There will be no hostility between you and us as long as you refrain from any sabotage or attacks on police establishments," said the warning.
Besides political instability, Egypt is also struggling with an economic crisis that has seen the Egyptian pound plunge to a record low against the US dollar.
Thursday, President Mursi blamed remnants of the Hosni Mubarak regime for trying to destabilise the country.
"The counter-revolution is being led by remnants of ousted president Hosni Mubarak's regime to obstruct everything in the country," he said.