However, the Brotherhood insisted violations were limited and should not affect the referendum's integrity.
The Freedom and Justice Party, the Brotherhood's political arm, said it hoped the passage of the constitution would be a "historic opportunity" to heal Egypt's divisions and launch a dialogue to restore stability and build state institutions.
If the violations are considered serious enough, there could be new votes in some areas that alter the results slightly.
One major concern in the aftermath of the constitutional turmoil is Egypt's deteriorating economy, which has been battered by the two years of turmoil and taken an added hit from renewed violence recently.
The referendum was conducted in two stages with the first vote on Dec. 15 and the second on Saturday. The Muslim Brotherhood and some media outlets have accurately tallied the outcome of past elections by compiling numbers released by electoral officials at thousands of individual polling stations shortly after voting closes.
Turnout for the vote was 32 percent of Egypt's more than 51 million eligible voters, according to the Muslim Brotherhood. That was significantly lower than other elections since the uprising ended in February 2011. The opposition has pointed to the low turnout as well as allegations of violations in the voting to cast doubt on the legitimacy of the referendum.
The Brotherhood said 64 percent voted "yes" to the constitution in a tally of both stages of voting. For Saturday's second stage only, the Brotherhood said 71 percent of those who voted said "yes" with 99 percent of polling stations accounted for.
As expected, it was a jump from the first round of voting when about 56 percent said "yes." The provinces that voted in the second round were known for being a base for Brotherhood supporters.
Only about eight million of the 25 million Egyptians eligible to vote in the second stage — a turnout of about 30 percent — cast their ballots. Some 32 percent of eligible voters participated in the first round.