The opposition National Salvation Front has already vowed that "the referendum is not the end of the road".
Weeks of sometimes violent protests have challenged the authority of President Mohammed Morsi, an Islamist from the resurgent Muslim Brotherhood who has been in power for six months.
Egypt's economy is struggling with the political uncertainty that has prevailed ever since the revolution in early 2011 that toppled Hosni Mubarak.
Morsi's Muslim Brotherhood argues that the new constitution it and fellow Islamists helped draft put to voters in a staggered referendum on December 15 and 22 will usher in a period of stability.
It says its unofficial tally shows 64% of voters backed it. But the opposition, a collection of leftwing, Christian, liberal and secular forces, has fought it. It contends the charter will undermine human rights and open a path to introducing strict sharia Islamic laws.