Egyptians returns to the voting booth Saturday to cast ballots in a national referendum on a draft constitution. Voting in Cairo, Alexandria and eight other provinces was conducted last weekend.
The constitution won narrow support in that part of the voting.
Though last weekend's vote was largely peaceful, Tutu, chairman of a diplomatic group called The Elders, called on Egyptians to express their grievances through peaceful means.
"What Egyptians have achieved in the last 22 months is extraordinary but if divisions are not addressed peacefully then the consequences will be long-lasting," he said in a statement.
Egypt witnessed several days of deadly demonstrations ahead of last weekend's vote. Some political groups and movements have expressed frustration with the direction of a country now led by the Freedom and Justice Party, a party formed by the Islamist Muslim Brotherhood.
Mohamed Morsi, the first democratically elected president in Egyptian history, hails from the Muslim Brotherhood.
The Muslim Brotherhood published a statement on its website from elections spokesman Mahmoud Abu-Shusha who said vote fraud allegations were part of a "hostile campaign."
"This talk about fraud and violations is completely void, impossible to happen," he said.