Egypt's Muslim Brotherhood has claimed victory in the first round of the country's bitterly divisive constitutional referendum, with opposition forces complaining of large-scale rigging and violations.

Unofficial results from Saturday's first round showed 56% approval to 43% rejection on a low turnout of 33%, with a clear no win in Cairo, one of the 10 governorates where polling took place. The referendum is to be held in the country's remaining 17 governorates next Saturday - where prospects for a no win are poorer.

The figures were reported by the Freedom and Justice party (FJP), the political wing of the Brotherhood, which has been accurate in previous elections.

If, as expected, the trend is confirmed, the referendum will bolster the Brotherhood's Mohamed Morsi, who was elected president on a 51% mandate last June. But no end is in sight to the country's grave political crisis.

Sit-in protests against the constitution were continuing on Sunday night in Cairo's central Tahrir Square and at the presidential palace in Heliopolis, where nine people were killed last week.

Gehad El-Haddad, a senior Brotherhood and FJP adviser, said: "We thank Allah and the people of Egypt for such honourable practice of democratic participation and although approval [is] lower than expected, [we are] glad it's yes."

The opposition National Salvation Front (NSF) claimed 66% were against the controversial draft basic law. It said it had detected "unprecedented rigging," including 750 violations. These included unstamped ballot papers, the names of deceased people on lists and the absence of observers at polling stations. The Egyptian Coalition for Human Rights reported the use of religious slogans and financial inducements for those voting yes.

Mohamed ElBaradei, the co-ordinator of the NSF, warned Morsi in Twitter messages: "In light of Egypt's evident, and dangerous, division, will you realize the necessity of being a president for all Egyptians? Country split, flagrant irregularities, low turnout, disillusion with Islamists on the rise. Illiteracy remains a hurdle."

Many Egyptians, alarmed by a growing budget deficit and the weakness of the pound against the US dollar, agree that stability will remain elusive through next month's second anniversary of the outbreak of the revolution which overthrew Hosni Mubarak, who had ruled Egypt for nearly 30 years.

"Even with all this rigging and intimidation the Brotherhood could only get 56%," Hisham Kassem, a political commentator, told the Guardian. "So next week will be much worse. Egypt is heading for disaster."

The referendum was largely peaceful, but violence erupted on Saturday night when the Cairo headquarters of the liberal Wafd Party, part of the NSF, came under attack. The Wafd accused the Salafist preacher Hazem Abu Ismail of being involved but he denied responsibility.

The hastily-arranged vote follows three weeks of protests and sporadic violence after Morsi adopted sweeping powers bypassing the judiciary and rushed through completion of the constitutional text in the constituent assembly.

In a highly polarised atmosphere the Brotherhood camp complains of a "counter-revolution" against a democratically-elected president by a coalition of anti-Islamist activists and so-called felool or remnants of the Mubarak regime.

But secular and liberal opponents, including many Muslims, insist that they object to his undemocratic and non-consensual behaviour and an ambiguous constitution flawed by what it says or implies about the role of Islam and clerical scholars, human and labour rights, the position of the still powerful army and other fundamental issues.

Independent Egyptian and foreign observers argue that a divided and disorganised opposition has seized too gleefully on Morsi's miscalculations and vacillation and now risks raising the stakes with an escalation of the crisis.

If passed, the constitution will pave the way for new parliamentary elections next year. The last national assembly, dominated by the Brotherhood and Salafis, was dissolved. In a new election, many now expect a decline for the Islamist vote and a better performance by more confident and united opposition candidates. "The Brotherhood will not be able to run the country," predicted Kassem. "They will end up with state failure."

The FJP said: "The Egyptian people have expressed their free will in the first stage of the constitutional referendum and have also proved to be highly aware. This is a genuine democratic process."