Morsi issued a decree on Nov. 22 that gave him immunity from oversight by Egyptian courts, which gave him unprecedented power in the country. Protesters demonstrated against this move.
Following the decree, Morsi introduced a draft constitution written by Islamist allies that was opposed by secular liberals who fear the country is moving toward a religious state.
Protesters and supporters of Morsi clashed over the past week near the presidential palace. Six have been killed and more than 700 reportedly injured in the conflicts.
Morsi offered to hold talks with the opposition to begin on Saturday. Opposition leaders said Morsi must drop the constitutional draft vote as a condition before talks could begin.
Egypt's election committee announced the postponement on Friday.
Hamdi said the weeklong voting by Egyptians abroad, which had been due to begin Saturday, will begin Wednesday instead.
But Legal Affairs Minister Mohammed Mahsoub said the administration was weighing several proposals. He said those included calling off the referendum and returning the draft to the constituent assembly for changes or disbanding the whole constituent assembly and forming a new one, either by direct vote or upon an agreement among the political forces.
Egypt's Vice President Mahmoud Mekki also told the pan-Arab television station Al-Jazeera that he had contacted leading democracy advocate Mohamed ElBaradei to join the president in dialogue. ElBaradei is leading the newly formed National Salvation Front, an umbrella group of liberals and youth groups that opposed Morsi's decrees.
He added that "until now the referendum is due Dec. 15" until agreement could be reached.
Before the announcement, after night fell, tens of thousands of Egyptian protesters pushed past barbed wire fences installed by the army and march on the presidential palace, calling for Morsi to "leave."
But on hearing the postponement of vote for Egyptians abroad, some expressed optimism.
"This looks like the beginning of a retraction," said 56-year-old doctor Mohsen Ibrahim. "This means Morsi may postpone the referendum. It looks like the pressure is working out."
But he warned that "if Morsi doesn't see the numbers of people protesting, then he will be repeating the same mistake of (Hosni) Mubarak."
Mubarak was unseated from a 30-year presidency in 2011 in a popular uprising against his regime.
The Associated Press contributed to this report.