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 documented more than 3,000 examples of "fraud, violations and organizational shortcomings" in the referendum's two rounds.
The voting's second round was held Saturday. The first round was held a week before.
"We would like the responsible party to investigate and report the conclusions before the final results of the referendum are announced," NSF leader and political scientist Amr Hamzawy said, referring to Egypt's High Elections Commission.
The official results were to be announced Monday. But Islamists claimed victory in advance and the state-run Middle East News Agency said the charter was approved by 64 percent of the vote.
About 16 million of the nation's more than 51 million voters cast ballots in the referendum over the two Saturdays, with the constitution winning by 4.5 million votes, preliminary figures indicated.
"We hope approving the new constitution would be a historic opportunity to reunite national forces, on the basis of mutual respect and sincere dialogue, in order to achieve stability in this homeland and to complete its constitutional institutions," the Freedom and Justice Party, the Muslim Brotherhood's political arm, said in a statement.
The opposition says the constitution gives Islamists too much power, ignores personal freedoms and disregards the rights of women and minorities, including Coptic Christians, who make up 10 percent of Egypt's population.
"The referendum is not the end game. It is only a battle in this long struggle for the future of Egypt," the NSF said in a statement Sunday. "We will not allow a change to the identity of Egypt or the return of the age of tyranny."
Morsi appointed 90 members to the Egyptian Parliament's upper house during the weekend, giving legislative powers to the chamber, known as the Shura, which means "consultation," until parliamentary elections scheduled for next year.
Christian and non-Islamist political lawmakers were among the appointees, the Los Angeles Times reported.
But the chamber's 270 seats remained dominated by Islamists, causing critics to dismiss Morsi's appointments as a cosmetic gesture, the newspaper said.