The coalition of seven groups made the call as the Muslim Brotherhood backers of President Mohamed Morsi claimed victory in Saturday's vote, saying unofficial tallies showed 56-percent approval of the draft constitution.
The rights groups complained that some voters were improperly turned away and some people illegally served as polling station monitors in place of judges. Prominent Egyptian opposition figure Mohammed ElBaradei joined the criticism on Twitter, posting a message saying irregularities were “flagrant,” and turnout was “low.”
The Muslim Brotherhood said turnout was about one-third of the 26 million people eligible to vote on Saturday. The first-round of the referendum was held in 10 of Egypt's 27 regions, including the two main cities of Cairo and Alexandria. A second-round will be held next Saturday in Egypt's remaining provinces, most of which are rural and religiously conservative, which opens the door for Islamists to cast multiple votes.
Some observers expect the second-round to boost the overall “yes” vote for the draft constitution, which requires only a simple majority for passage.
Egypt's main liberal opposition coalition, the National Salvation Front, said Sunday it will not accept any unofficial referendum results.
Saturday's vote was not without violence, with more than 100,000 Egyptian troops deployed to prevent violence. But as the polls closed, some Islamists assaulted the Cairo offices of a liberal newspaper affiliated to the opposition Wafd party.
Opposition activists note the constitution will erode civil liberties because it rests on the role of Islamist Sharia law and does not mention women's rights. An Islamist-dominated constituent assembly drafted the document last month after liberal and Christian members walked out, complaining they were being ignored.
Islamist supporters of the draft constitution say its passage in a referendum is an important step toward Egypt's transition to "democracy," almost two years after a popular uprising toppled longtime President Hosni Mubarak.
The controversy over the constitution sparked rival mass protests by opposition and Islamist activists earlier this month. At least eight people were killed in street battles among demonstrators. VoA.