week, polls were held in areas which, analysts expected, would give another "yes" vote, Al Jazeera reported.
The vote took place in 17 of Egypt's 27 provinces with about 25 million eligible voters.
It came a day after violent clashes between supporters and opponents of President Morsi in the Mediterranean port city of Alexandria.
The violence, which injured several dozen people, is the latest episode in more than four weeks of turmoil over the President's sweeping powers and the Constitution.
The proposed Constitution has deeply divided Egypt, with supporters of Morsi backing the new document while mainly liberal opponents decrying it as too partisan.
The first phase on December 15 produced a "yes" majority of about 56% with a turnout of some 32%, according to unofficial results.
A comfortable "yes" majority would strengthen Morsi and his Islamist backers.
The opposition, however, said voting in the first round was littered with electoral abuses. But officials overseeing the poll have said there were no major irregularities.
In an interview to Al Jazeera on Saturday, Seif Allah al-Khawanky, of the National Salvation Front, said the low turnout is "an act of showing the rejection to this project, which they don't believe in."
"The legitimacy of this referendum is really questionable," al-Khawanky said. "No one was represented except one group in drafting this Constitution."
Morsi and his backers say the new Constitution is needed to seal a transition from decades of military-backed autocratic rule, while opponents say it ignores the rights of women and minorities, including the 10% of Egyptians who are Christian.
A leading Muslim Brotherhood official dismissed concerns that the new Constitution will lead to greater division or upset Egypt's fragile political balance.
"Egypt is not divided and is not facing any internal dangers," said Essam El-Erian, the deputy head of the Brotherhood-affiliated Freedom and Justice Party.
"In reality Egypt is now on the verge of building a new political system that will be open to all political forces," he said.
Widespread demonstrations erupted when Morsi awarded himself sweeping powers on November 22, and then fast-tracked the Constitution through a drafting assembly dominated by his Islamist allies and boycotted by many liberals.