‘‘The results of the referendum are for sure because of the rigging, violations and mismanagement that characterized it,’’ the National Salvation Front said.
It alleged the vote was marred by lack of complete judicial supervision, which led to overcrowding that pushed down the voting rate. It also charged there was interference by those who were supposed to be supervising the vote, with some instructing people to vote ‘‘yes.’’ Many judges who traditionally supervise elections boycotted supervising the vote.
‘‘We don’t think the results reflect the true desires of the Egyptian people,’’ Khaled Dawoud, the front’s spokesman, told The Associated Press.
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.
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.
The Front said that regardless of the results, it welcomed the participation of many who rejected the constitution and refused to consider it a vote on Islamic law. The group vowed to continue to ‘‘democratically’’ work to change the constitution and praised the high turnout of women.
The Islamists say Islam is core to Egypt’s identity and they view the constitution as a foundation to move forward, elect a parliament and build state institutions.
The new constitution will come into effect once official results are announced.
Once that happens, Morsi is expected to call for the election of parliament’s lower chamber, the more powerful of the legislature’s two houses, within two months.
The opposition said that even though it is challenging the results of the referendum, it will continue to prepare for the upcoming parliamentary elections.
Until the lower chamber is elected, the normally toothless upper house, or Shura Council, will have legislative powers.
On Sunday, Morsi appointed 90 new members to the Islamist-controlled Shura Council as part of his efforts to make the council more representative. The new appointments included at least 30 Islamists and a dozen Christians. They also include eight women, four of them Christians.
The opposition front said it did not want its members nominated to the Shura Council, now made up of 270 members.