Voting on the controversial Islamist-backed draft charter is due to start on Saturday with a second round scheduled for a week later.
Egyptians abroad have already started casting their votes in embassies and consulates, the official MENA news agency said.
Mass demonstrations for and against the referendum called by Islamist President Mohamed Morsi took place in Cairo late on Tuesday.
But there was no repeat of the violent clashes between Morsi supporters and foes last week that left eight people dead and hundreds injured.
The army, which has deployed troops and tanks to protect the presidential palace in Cairo, said it was postponing to an unspecified “later date” talks it had scheduled for Wednesday between Morsi and the opposition.
Responses to its invitations to the dialogue “were not at the level wished for,” the military explained in a statement on its official Facebook page.
The opposition National Salvation Front, which said it had agreed to take part in the talks, appealed to its supporters to vote ‘no’ in the referendum on the draft charter.
It warned it could call for a boycott if Morsi’s government failed to meet tough conditions.
“We call to Egyptians to go to polling stations to refuse the proposed constitution and to vote no,” it said in a statement read by a spokesman at a news conference.
That position would harden to a boycott call if Morsi’s government did not organise the voting on a single day — this coming Saturday — as originally planned, and if judges and international poll monitors did not oversee it.
Those conditions appeared near-impossible for Morsi to meet. A key group of judges has already said it will not oversee the vote. Pro-Morsi judges would be stretched too thin to monitor the referendum in one day.
Egyptian citizens were divided over the referendum.
“I’m voting yes,” said Mohammed Hassan, a 28-year-old Cairo resident who said Morsi’s Muslim Brotherhood had been unfairly maligned.
“The Muslim Brotherhood is good. No one has given them a chance. They’ve been in power for five months compared to 30 years for Mubarak,” he said, referring to toppled leader Hosni Mubarak.
Mohammed Ibrahim Sayyid, in his 40s and sipping coffee in a cafe, felt differently.
“We don’t like what’s happening. We don’t want another Afghanistan because of the Muslim Brotherhood. We are a big, diverse country of 80 million people. There shouldn’t be one party ruling,” he said.
Hamdi Imam, a street bookseller in his 50s, said: “I’m not going to vote because the constitution has blood on it…. The Muslim Brotherhood will destroy the country.”
Michael Wahid Hanna, a political analyst at US think-tank The Century Foundation, told AFP that, given the Muslim Brotherhood’s proven ability to mobilise grassroots support, the odds were good that the referendum would pass, although it was not “an absolute certainty.”
If it did pass, “it would be problematic for the future” because it would ensnare all of Morsi’s future decisions in political polarisation.
“If you overreach in this fashion, it will provoke a reaction and extend instability,” Hanna said, warning of “the spectre of violence”.
The military has already said it fears the Arab world’s most populous country is headed for a disastrous “dark tunnel” unless the two sides talk. It has warned it will not allow the situation to worsen.
The United States said there were “real and legitimate questions” about the referendum process and urged Egypt’s army, which it gives $1.3 billion in aid each year, “to exercise restraint, to respect the right of peaceful protest.”