Egyptians have narrowly backed an Islamist constitution in the first round of a referendum over the contentious draft, unofficial figures showed today, even as the opposition accused the Muslim Brotherhood of "vote rigging" and rights groups demanded a re-poll.

Rival camp officials said the Egyptians have voted narrowly in favour of the draft, citing the unofficial figures, after the first round of the two-stage referendum held yesterday.

The Muslim Brotherhood said the group's tallies showed that 56.5 per cent of voters had supported the constitution, while 43 per cent had voted 'no'.

The figures had fallen short of the landslide President Muhammed Mursi had been hoping for. The Brotherhood's Freedom and Justice Party (FJP) had representatives posted at almost every polling place in the 10 areas.

Opposition officials also said that the vote appeared to have narrowly gone in favour of the 'yes' camp, the Al Jazeera news channel reported.

Majority of the voters in the capital Cairo have rejected the draft, with 57 per cent opposing it. In Gharbiya governorate, 52 per cent opposed the draft, the Egypt Independent newspaper reported.

However, the support for the draft was received in governorates like South Sinai (63 per cent), North Sinai (82 per cent), Sohag (79 per cent) Assiut (76 per cent) Sharqiya (66 per cent) and Aswan (74 per cent), it said.

The second round of the referendum is scheduled for next Saturday, after which the official result would be announced.

The National Salvation Front, the umbrella opposition group, said it was deeply concerned about irregularities, such as directing voters outside polling stations to vote 'yes'.

In a statement, the group expressed "deep concern... Over the number of irregularities and violations in the holding of the referendum". This, it alleged, pointed to a "clear desire for vote-rigging by the Muslim Brotherhood".

The allegations also include; unsealed ballot papers and absence of judges to monitor the polls.

Meanwhile, representatives of seven rights groups demanded a re-poll of the first phase of the referendum, alleging that the election commission did not investigate thousands of complaints on violations and irregularities.

"We call on the election commission to avoid these violations in the second round and repeat the first round," said a statement by the seven groups. "The vote counting took place took place in darkness," said Negad Borai, the head of one of the groups.

The referendum came after violent clashes that left eight people dead on December 5 amid a highly polarised political climate. Soldiers joined police outside polling stations to secure referendum after deadly protests.

Later on Saturday, riot police fired tear gas to dispersed dozens of hardline Mursi supporters who attacked the central Cairo headquarters of the opposition liberal Wafd Party with fireworks and stones.

Mursi and his supporters say the constitution is vital in order to move forward with the country's democratic transition. Opponents say that the basic law is too heavily influenced by religion, and that it tramples on minority rights.

Egypt's Constituent Assembly on November 30 in a marathon session approved the draft constitution imposing Islamic values, a move opposed by Liberals as an attempt to restrict freedom of speech and religion in the country.

The articles passed, stipulated that Islam is the religion of the state, and the principles of Sharia, or Islamic law, are the "main source of legislation".

This week, Egyptian Central Elections Commission announced that the vote, initially set only for December 15, will take place on December 15 and a week later on December 22.

In order to pass, the constitution must be approved by more than 50 per cent of voters who cast ballots. A little more than half of Egypt's electorate of 51 million were eligible to vote.

The present political turmoil began after President Mursi granted himself absolute powers through a November 22 decree that had put his decisions beyond judicial review, a move which gained him titles like "dictator" and "Pharaoh". Mursi tried to calm protests by annulling the decree, but decided to go ahead with the referendum.