Initial results indicate the majority of the population voted for the amendments, the Ahram Online Web site said Sunday.
Attiya, chairman of the Supreme Judicial Committee that supervised the vote, described Saturday's turnout as unprecedented, the Egyptian daily al-Masry al-Youm reported Sunday.
"Egyptians restored their dignity after the 25 January Revolution ... each citizen is now aware of the value of his vote," Attiya told the newspaper, adding the results will reflect the "voters' will."
At least 25 million of the 40 million eligible to vote participated in the balloting to change Egypt's constitution, Attiya said estimating more than 65 percent supported the referendum, Ahram Online reported.
In northern Sinai, 85 percent of voters favored amendments, and 81.5 percent in Luxor. A source told the Web site that in southern Cairo 65 percent of voters voted for change.
Saturday evening, Muslim Brotherhood Supreme Guide Mohamed Badie said his group would accept the results of the referendum regardless of the outcome. "I congratulate Egypt for this great day. We are happy that Egyptians are so ecstatic and it is the voters' say that will determine the future of Egypt, which has finally regained its freedom," Ahram Online quoted him saying at a news conference.
The amendments will allow the country to move toward presidential and parliamentary elections and the transfer of power from the military to the civilian body.