This comes as at least 51 people were killed in the capital Cairo.
The Muslim Brotherhood says its members were fired on at a sit-in for ousted President Mohammad Morsi. The army says it responded to an armed provocation.
Mr Morsi, an Islamist and Egypt’s first freely elected leader, was removed from office by the army last week after mass protests.
His supporters accuse the military of staging a coup, but his opponents say the move is the continuation of the revolution that deposed President Hosni Mubarak in 2011.
Mr Mansour issued the decree late on Monday.
It says that a panel to amend the constitution – which was suspended last week – would be formed within 15 days.
The changes would then be put to a referendum – to be organised within four months.
This would lead to parliamentary elections – which could be held early in 2014.
Finally, presidential elections would be called once the new parliament convenes.
The Muslim Brotherhood has so far made no public comment on the proposed timetable.
Mr Mansour’s move comes amid continuing mass protests by both supporters and opponents of Mohammad Morsi.
The situation will have to improve radically if Mr Mansour’s timetable for elections is not to prove hopelessly unrealistic, the BBC’s Jim Muir in Cairo reports.
In the meantime, the focus will remain on trying to prevent another explosion of violence and to agree on an interim prime minister to form a transitional government to stabilise the country and prepare for elections.
Meanwhile, the United States has condemned the violence in Egypt, calling for “maximum restraint”.
There were conflicting reports over what happened outside the Presidential Guard barracks in Cairo on Monday morning.
The Muslim Brotherhood put the number of dead at 53, and said children were among the victims.
It said the army raided its sit-in at about 04:00 (02:00 GMT) as protesters were praying.
Later, in an emotional news briefing, members of the Muslim Brotherhood accused military chief Gen Abdul Fattah al-Sisi of being “an assassin and a butcher”.
The health ministry said at least 51 people were killed and 435 people wounded.
Speaking to journalists, army spokesman Col Ahmed Mohammed Ali said a group armed with live ammunition, petrol bombs and stones had attacked security forces.
He said that two police and one soldier were killed in the exchange of fire. Eight soldiers were critically wounded.
The spokesman added that one soldier had been shot through the top of the head from above, indicating that snipers were firing from high buildings.
Col Ali also disputed claims that children had died, saying pictures of dead children posted on the internet were in fact images taken in Syria in March.
Mr Morsi is believed by the Muslim Brotherhood to be held at the barracks, but the military says he is elsewhere.