On the eve of polling, clashes in Egypt's second city Alexandria injured 62 people as stone-throwing mobs torched vehicles, underlining the turmoil gripping the Arab world's most populous nation.
On December 5, eight people were killed and hundreds injured in clashes between rival demonstrators outside the presidential palace in Cairo.
Some 250,000 police and soldiers were deployed to provide security during the referendum. The army has also positioned tanks around the presidential palace since early this month.
The proposed charter was expected to be adopted after already garnering 57 percent support in the first round of the referendum a week ago.
But the slim margin and a low first-round turnout have emboldened the opposition, which looks likely to continue its campaign against Morsi and his Muslim Brotherhood backers.
Long queues were reported at many polling stations on Saturday.
Electoral officials announced they were extending voting by four hours, to 11:00 pm (2100 GMT), as they did in the first round.
At one polling station in Giza, southwest Cairo, 50-year-old housewife Zarifa Abdul Aziz said: "I will vote 'no' a thousand times... I am not comfortable with the Brotherhood and all that it is doing."
Rana Jaber, 24, said she was voting against a draft constitution she believed would "undermine the rights of workers and children."
However 19-year-old law student Ahmed Mohammed said he voted yes because "I am convinced it contains the best of the 1971 constitution," the document that the new charter will replace.
Mohamed Mamza, a 49-year-old driver, said: "I am voting 'yes' because Egypt needs a constitution to be stable."
The text was drafted by a panel dominated by the Muslim Brotherhood and ultra-orthodox Salafist groups. Christians and liberals boycotted the process in protest at changes they saw as weakening human rights, especially those of women.
Morsi had to split voting over two successive Saturdays after more than half of Egypt's judges said they would not provide the statutory supervision of polling stations.
The main opposition group, the National Salvation Front, launched a last-ditch campaign to vote down the charter after deciding that a boycott would be counter-productive.
But it and Egyptian human rights groups alleged the first round was marred by fraud, setting up a possible later challenge to the results. They called news conferences for Sunday to give their observations of the second round of polling.
Preliminary tallies from the final round were expected early Sunday. Full official results will be released "two days after the end of polling," the electoral commission said, according to the official MENA news agency.
If, as expected, the new constitution is adopted, Morsi will have to call parliamentary elections within two months, to replace the Islamist-dominated assembly ordered dissolved by Egypt's top court in June.