But, despite their presence, there are reports of a fresh outbreak of stone-throwing between the two sides.
Egypt is seeing growing unrest over a controversial draft constitution.
The government insists that a referendum will go ahead this month.
The head of Egypt‘s Republican Guard said the forces deployed outside the presidential palace on Thursday had been sent there to separate supporters and opponents of President Morsi.
General Mohamed Zaki called for calm, telling the state-run Middle East News Agency: “The armed forces, and at the forefront of them the Republican Guard, will not be used as a tool to oppress the demonstrators.”
The BBC’s Jon Leyne in Cairo says the clashes between supporters and opponents of Egypt‘s new president are possibly the most dangerous development in Egypt’s growing political crisis.
Our correspondent says the violence, which opposition leaders accused Mr Morsi’s Islamist Muslim Brotherhood movement of organising, was ominously reminiscent of the tactics used by former President Hosni Mubarak during the revolution.
Supporters of Mr Morsi responded to a call to rally outside the presidential palace, in the suburb of Heliopolis, on Wednesday afternoon.
The mainly secular opponents of the president were already staging a sit-in protest there, after tens of thousands of them besieged the palace on Tuesday.
Stones and petrol bombs were thrown and there were reports of gunfire as Morsi supporters dismantled some of the tents set up by their opponents.
The Brotherhood later called on all sides to “withdraw at the same time and pledge not to return there given the symbolism of the palace”.
Disorder was also reported in other cities, with Muslim Brotherhood offices attacked in Ismailia and Suez.
Speaking on Wednesday, Vice-President Mahmoud Mekki said the vote on the draft constitution was still scheduled for 15 December, but that the “door for dialogue” remained open, indicating that changes could be made to the document later.
Critics say the draft was rushed through parliament without proper consultation and does not do enough to protect political and religious freedoms and the rights of women.
The draft added to the anger generated by Mr Morsi passing a decree in late November which granted him wide-ranging new powers.
Four of Mr Morsi’s advisers resigned on Wednesday in an apparent protest. Three others did so last week and Egypt’s Mena news agency reported a further resignation on Thursday.
Our correspondent says the government has been speaking for some time about the need for dialogue, but has offered few concrete concessions which would end the crisis.
Mr Morsi adopted sweeping new powers in a decree on 22 November, and stripped the judiciary of any power to challenge his decisions.
Mr Morsi, who narrowly won Egypt’s first free presidential election in June, says he will give up his new powers once the new constitution is ratified.