Official results of the referendum are not expected until Monday (local time). If the unofficial numbers are confirmed, it will be a victory Islamist President Mohammed Morsi, who is from the Brotherhood.
But the opposition allegations look likely to prolong the fight. Beyond allegations of fraud, the opposition will likely challenge new laws issued on the basis of the constitution as well as Morsi's economic policies.
"The referendum is not the end game. It is only a battle in this long struggle for the future of Egypt," said the National Salvation Front, the main opposition group. "We will not allow a change to the identity of Egypt or the return of the age of tyranny."
The opposition claims the new constitution seeks to enshrine Islamic rule in Egypt and accuses the Islamists of trying to monopolize power.
Critics say it does not sufficiently protect the rights of women and minority groups and empowers Muslim clerics by giving them a say over legislation. Some articles were also seen as tailored to get rid of Islamists' enemies and undermine the freedom of labor unions.
The latest political battle began with Morsi's Nov. 22 decrees that gave him powers to protect the Islamist-dominated panel writing the constitution and dismiss the country's top prosecutor, a holdover from the Mubarak era.
Although Morsi subsequently rescinded the powers that gave him immunity from judicial oversight, his decision to replace the prosecutor general was viewed by many in the judiciary as trampling over their powers. Hundreds of prosecutors held a rally Sunday demanding the new, Morsi-appointed prosecutor general quit, days after he retracted his resignation claiming it was rendered under pressure.
The prosecutors said in a news conference that they will be on strike until he quits.
Scores of lawyers who support Morsi's decision held an earlier rally, demanding that the top prosecutor stay, and accusing the opposition of being "thugs."
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.
Adding to the anxiety, state television reported on Saturday amidst voting on the referendum that the central bank governor had resigned, then retracted the report. The governor turned up at a meeting of the government's economic team Sunday in an apparent attempt to quell nervousness over the state of the economy.
The government stressed the urgency of stability.
"The financial and economic situations are dire," government spokesman Alaa el-Hadidi said, according to comments published by the state news agency MENA. With the referendum behind, el-Hadidi said economic policies must be at the center of attention, adding that the government will work to improve the investment environment to attract foreign investors.
The government had to postpone a request for $4.8 billion of IMF loans, putting off unpopular tax increases and reforms to after the referendum for fear they would only stoke political tensions.
A day before the official results of the constitution are expected, the opposition front said it filed complaints to the country's top prosecutor and the election commission asking for an investigation.
"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.
- AP
