Polling at most stations went smoothly, but eight people were killed in clashes outside Cairo between Morsi supporters and police and anti-Morsi groups, security officials said.
The violence highlighted the government's precarious grip on the most populous Arab nation, still reeling from Morsi's ouster and a crackdown on his supporters.
An Islamist coalition led by the former president's Muslim Brotherhood had urged protests and a boycott of the two-day vote, which ends on Wednesday.
A small bomb exploded outside a Cairo court shortly before polls opened without causing any casualties, as hundreds of thousands of soldiers and police deployed to guard polling stations.
The interior ministry had pledged to confront any attempt to disrupt voting.
Three people were killed in the town of Kerdasa, south of Cairo, and five died in central and southern Egypt when protesters clashed with police and civilian opponents.
Before the voting ended, at least 140 people, including some Brotherhood members, had been arrested for disrupting the polling in some areas, security officials said.
Defence minister Abdel Fattah al-Sisi, the general who overthrew Morsi, visited a polling station at a Cairo school to inspect security preparations on Tuesday.
"Work hard. We need the referendum to be completely secured," he told soldiers guarding the school.
The government hopes a large turnout in favour of the constitution will bolster its disputed authority, while Sisi will monitor it for an "indicator" of his popularity, an official close to the general said.
Interim president Adly Mansour called for a big turnout.
"The people must prove to dark terrorism that they fear nothing," he said after casting his vote.
"The voting is not only for the constitution, but also for the roadmap, so the country can have an elected president and a parliament."
Mansour's government has pledged the referendum will be followed by parliamentary and presidential elections.
Security forces deployed across the country amid fears recent attacks by militants would deter voters.
At one polling station for women, dozens queued to cast their ballots, some waving Egyptian flags and chanting pro-military slogans.
"We must be with our police and army so that no one can terrorise us. Even if a bomb exploded in my polling station, I would vote," said Salwa Abdel Fattah, a 50-year-old gynaecologist.
It is unclear how many Egyptians will turn out to vote, but the constitution appears certain to pass.
Charter bolsters army's powers
The charter has done away with much of the Islamist-inspired wording of Morsi's constitution, suspended on his overthrow, and its supporters say it expands women's rights and freedom of speech.
But it has bolstered the military's powers, granting the army the right to appoint the defence minister for the next eight years and to try civilians for attacks on the armed forces.
The runup to the vote was marred by a crackdown on Morsi's supporters and arrests of activists who campaigned for a "no" vote.
The capital has been festooned with banners urging Egyptians to vote "yes", often featuring military motifs such as a general's hat, an allusion to Sisi.
Many Islamists revile Sisi as the man who overthrew the country's first freely elected and civilian president, but the general is adored by millions who took to the streets to demand Morsi's resignation.
He is widely expected to run for president, and has said he would stand if there was "popular demand," state media reported this week.
The authorities are worried a low turnout would empower their Islamist opponents and cast further doubts on their legitimacy, analysts say.
"Prove to the world that what happened was a popular revolution," interior minister Mohamed Ibrahim said during a visit to a polling station.
Backers of the constitution are hoping it will receive the support of at least 70 percent of votes cast.
Morsi's constitution passed with 64 percent of the vote, but on a turnout of barely 33 percent of the country's 53 million voters.
Since Morsi's ouster, at least 1,000 people have been killed, most of them Islamists, and thousands more detained.
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The violence highlighted the government's precarious grip on the most populous Arab nation, still reeling from Morsi's ouster and a crackdown on his supporters.
An Islamist coalition led by the former president's Muslim Brotherhood had urged protests and a boycott of the two-day vote, which ends on Wednesday.
A small bomb exploded outside a Cairo court shortly before polls opened without causing any casualties, as hundreds of thousands of soldiers and police deployed to guard polling stations.
The interior ministry had pledged to confront any attempt to disrupt voting.
Three people were killed in the town of Kerdasa, south of Cairo, and five died in central and southern Egypt when protesters clashed with police and civilian opponents.
Before the voting ended, at least 140 people, including some Brotherhood members, had been arrested for disrupting the polling in some areas, security officials said.
Defence minister Abdel Fattah al-Sisi, the general who overthrew Morsi, visited a polling station at a Cairo school to inspect security preparations on Tuesday.
"Work hard. We need the referendum to be completely secured," he told soldiers guarding the school.
The government hopes a large turnout in favour of the constitution will bolster its disputed authority, while Sisi will monitor it for an "indicator" of his popularity, an official close to the general said.
Interim president Adly Mansour called for a big turnout.
"The people must prove to dark terrorism that they fear nothing," he said after casting his vote.
"The voting is not only for the constitution, but also for the roadmap, so the country can have an elected president and a parliament."
Mansour's government has pledged the referendum will be followed by parliamentary and presidential elections.
Security forces deployed across the country amid fears recent attacks by militants would deter voters.
At one polling station for women, dozens queued to cast their ballots, some waving Egyptian flags and chanting pro-military slogans.
"We must be with our police and army so that no one can terrorise us. Even if a bomb exploded in my polling station, I would vote," said Salwa Abdel Fattah, a 50-year-old gynaecologist.
It is unclear how many Egyptians will turn out to vote, but the constitution appears certain to pass.
Charter bolsters army's powers
The charter has done away with much of the Islamist-inspired wording of Morsi's constitution, suspended on his overthrow, and its supporters say it expands women's rights and freedom of speech.
But it has bolstered the military's powers, granting the army the right to appoint the defence minister for the next eight years and to try civilians for attacks on the armed forces.
The runup to the vote was marred by a crackdown on Morsi's supporters and arrests of activists who campaigned for a "no" vote.
The capital has been festooned with banners urging Egyptians to vote "yes", often featuring military motifs such as a general's hat, an allusion to Sisi.
Many Islamists revile Sisi as the man who overthrew the country's first freely elected and civilian president, but the general is adored by millions who took to the streets to demand Morsi's resignation.
He is widely expected to run for president, and has said he would stand if there was "popular demand," state media reported this week.
The authorities are worried a low turnout would empower their Islamist opponents and cast further doubts on their legitimacy, analysts say.
"Prove to the world that what happened was a popular revolution," interior minister Mohamed Ibrahim said during a visit to a polling station.
Backers of the constitution are hoping it will receive the support of at least 70 percent of votes cast.
Morsi's constitution passed with 64 percent of the vote, but on a turnout of barely 33 percent of the country's 53 million voters.
Since Morsi's ouster, at least 1,000 people have been killed, most of them Islamists, and thousands more detained.
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