President Mohammed Morsi has congratulated Egyptians for endorsing a new constitution and urged all parties to join him in a national dialogue.
In a TV address to the nation, Mr Morsi said the economy was a priority and that changes to the cabinet would be made if necessary.
Some 63% backed the constitution in the controversial referendum.
But opponents say the document is too Islamist and have rejected the call for dialogue as “lacking seriousness”.
A spokesman for the main opposition group said protests would be held in Tahrir Square in Cairo and elsewhere on 25 January, the second anniversary of the uprising against Hosni Mubarak’s rule.
In his first address to the nation since he signed the new constitution into law, Mr Morsi said that this was a historic day.
Egypt, he said, had a free constitution that had not been imposed by an occupier, a king or a president.