peacefully and renounce violence", said a message posted on his Twitter account.
At least seven people died in Friday's anti-government protests, according to the health ministry, six in Suez and one in Ismailiya, in the northeast, while 456 people had been injured in the unrest.
The interior ministry said 95 of its officers had been injured.
The Islamist president, of the Muslim Brotherhood, said police officers were among the dead. He blamed the violence on criminals and said they would be tracked down and brought to justice.
After the sweeping changes of 2011, the Arab world's most populous nation is struggling to find a balance between its elected leadership and opponents who accuse it of betraying the goals of the revolution.
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.
Doctors at Suez Hospital told AFP at least five people had been shot in the chest and stomach after fierce clashes broke out between protesters and police in the canal city.
In the neighbouring province of Ismailiya, protesters stormed the governorate headquarters, setting fire to a room used by security services and looting furniture and equipment, an AFP reporter said.
Demonstrators had earlier set fire to the Muslim Brotherhood headquarters in Ismailiya, the reporter said. Black smoke billowed from the windows of the apartment housing the movement's Freedom and Justice Party (FJP) offices.
In the Mediterranean city of Damietta, protesters surrounded the governorate building and blocked traffic in the area.
In the Nile Delta city of Kafr el-Sheikh they stormed the courtyard of the building and clashed with police.
In Cairo, police fired tear gas at protesters outside the presidential palace, where clashes between Morsi's allies and foes in December killed several people.
Army and police forces were deployed to protect the building, which houses the information ministry as well as state television and radio. The protesters outside blocked traffic as marches swarmed the capital.
Protesters set fire to tyres and blocked traffic in both directions on the 6 October bridge, a flyover that connects east and west Cairo.
Some also blocked the underground metro at several stations in central Cairo, paralysing the public transport used by millions every day.
In Egypt's second city Alexandria, as demonstrators clashed with the security forces, some protesters set fire to tyres, witnesses said.
"The smoke is black, there is a lot of gas. There are people on the ground because they can't breathe," one of the protesters, who gave his name only as Rasha, told AFP.
Earlier in the day, thousands marched across Egypt, notably converging on Tahrir Square in Cairo -- the focal point of the 2011 revolution -- a day after clashes between police and protesters who attempted to pull down a cement wall blocking off the square.
In one street off Tahrir, dozens of youths threw rocks over the wall erected by security forces as police responded with tear gas, AFP journalists said. In the square itself, thousands of protesters chanted anti-Brotherhood slogans.
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 opposition had called for mass protests under the same slogan that brought Egypt to its feet in 2011: "Bread, freedom, social justice."
The Muslim Brotherhood did not officially call its own rallies, instead marking the second anniversary by launching a charitable and social initiative dubbed "Together we will build Egypt".