After the first round of voting last 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 per cent with a turnout of some 32 per cent, 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 today, 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." (MORE)
