The main secular opposition coalition, the National Salvation Front, led by Nobel Peace laureate and former International Atomic Energy Agency chief Mohamed ElBaradei, said it found "unprecedented rigging" in all participating districts in the referendum's first round Saturday.
The Front demanded Saturday's results be canceled and the election's first phase re-run.
Unofficial result estimates of the first phase of the constitutional referendum President Mohamed Morsi ordered showed charter approval was ahead 56 percent to 44 percent, with 31 percent of Egyptians voting, Egyptian newspaper al-Ahram reported.
"It's hard to imagine that any respectable country would pass a constitution rejected by 44 percent of society, especially when turnout rates failed to exceed 31 percent," Mohamed Adel, a member of the opposition April 6 Youth Movement, said in a statement.
Ahmed Oqeil, a member of the Muslim Brotherhood's Freedom and Justice Party, said the results are totally legitimate.
"The opposition is trying to get people to believe that a 56 percent approval rate is not sufficient for the charter to pass, which is not the case," Oqeil told al-Ahram. "No constitution can garner a 90 percent approval rate. A 50-plus-1 approval rate is all that is necessary."
The referendum's second phase is set for Dec. 22.
Meanwhile, Egypt's new top prosecutor resigned, state media said, after judges and lawyers argued Morsi unlawfully named him under his power-grab decree.
Prosecutor-General Talaat Ibrahim Abdallah, former leader of the movement for judicial independence under ousted President Hosni Mubarak, said in his resignation letter he quit 25 days after taking the job so he could "return to his work in the judicial system," state news agency MENA reported.
The letter is expected to be submitted before the Supreme Judicial Council Sunday, al-Ahram reported.
But al-Ahram said Abdallah succumbed to mounting pressure from judges and prosecutors.
Hundreds of judges and prosecuting attorneys staged a protest outside his office Monday, saying Abdallah's appointment by Morsi Nov. 22 -- right after Morsi issued a decree granting himself broad powers above any court as the guardian of Egypt's revolution -- was unlawful.
They said the Supreme Judicial Council was the only authority with power to nominate a prosecutor, in line with Egypt's separation of powers.
Morsi had no immediate comment on the resignation.
On Nov. 22 Morsi replaced unpopular Prosecutor-General Abdel Meguid Mahmoud with Abdallah.
Mahmoud was a Mubarak appointee widely criticized for failing to win stronger sentences against Mubarak and his associates, and against abusive police officers, in the uprising that ousted Mubarak.
Mubarak was sentenced to life in prison for overseeing the killing of protesters, but the verdict found no direct evidence of his involvement, paving the way for an appeal. Morsi Nov. 22 ordered a retrial of Mubarak after removing Mahmoud and appointing Abdallah.
At the end of the day Monday -- after protests that included judges and lawyers trying once to enter Abdallah's office to demand a meeting only to be turned back by security forces -- Abdallah spokesman Adel el-Said said Abdallah had resigned, al-Ahram reported, adding Said showed the protesters Abdallah's handwritten resignation letter.
Abdallah then left his office escorted by security forces, the newspaper said. Protesters broke out into cheers.