Opposition groups in Egypt have called for nationwide protests Tuesday, alleging poll violations in the first round of a two-stage referendum on a draft constitution, held Dec.15, while seeking a better supervision of the second round of ballot slated to be held Dec. 22.

In the districts that voted Saturday, which include the opposition strongholds of Cairo and Alexandria, 56.5 percent voted in favor, a senior official from President Mohamed Morsi’s Freedom and Justice Party (FJP) told Reuters.

Though an opposition politician conceded that the "yes" camp appeared to have won the first round, the opposition National Salvation Front (NSF) said voting abuses meant a rerun was needed, without explicitly challenging Muslim Brotherhood's vote tally, Reuters has reported.

The strongest "no" vote was in Cairo, counting 68 percent, while in Egypt's second largest city, Alexandria, nearly 56 percent voted “yes,” according to the official website of Egypt's state television.

The NSF coalition said it would "not recognize any unofficial result," and would wait for the formal tally after the second round of voting, Al Jazeera has reported.

It called on Egyptians to "take to the streets on Tuesday to defend their freedoms, prevent fraud and reject the draft constitution."

NSF leader Mohamed ElBaradei, a former chief of the U.N. nuclear energy agency, tweeted: "Country split, flagrant irregularities, low turnout, disillusion w(ith) Islamists on the rise. Illiteracy remains a hurdle."

The opposition, which first called for a boycott of the referendum, switched Thursday to campaign for a no vote.

Violence was reported during voting, but Saturday was rather peaceful compared to the clashes Friday, between rival factions armed with clubs, knives and swords in the streets of Alexandria.

Rights groups expressed concern about the fairness of the process, saying opponents of the charter, particularly women and Christians were not allowed to vote. Some polling stations were reportedly opened late and employed fake supervisors, while officials coerced people to vote "yes."

A joint statement by seven human rights groups urged the referendum's organizers "to avoid these mistakes in the second stage of the referendum and to restage the first phase,” Reuters has reported.

The head of the referendum commission said the official results will be announced after the second and last round next Saturday, suggesting that reports of polling violations will not stop the process, at least at this stage, the Associated Press reported.

Morsi and his Islamist supporters say the constitution is vital to move Egypt's democratic transition forward. But the president’s liberal, secular opponents argue that it does not represent the aspirations of all Egyptians because of provisions that give Muslim clerics a role in shaping laws. The main opposition coalition also demands more safeguards for women and minorities.