Egypt's opposition has called for an investigation into allegations of fraud in the referendum on the country's contentious draft constitution, after the Muslim Brotherhood claimed 64% of voters had backed the new charter.

Official results from the two-round poll are scheduled for release on Monday, but the opposition allegations are likely to prolong months of bitter political clashes, which have at times erupted into deadly street battles.

President Mohamed Morsi's Freedom and Justice party, the Brotherhood's political arm, said an unofficial tally of the vote showed a majority of the population had backed the constitution. "We hope approving the new constitution would be an historic opportunity to reunite national forces, on the basis of mutual respect and sincere dialogue, in order to achieve stability in this homeland and to complete its constitutional institutions," the FJP said.

But the opposition National Salvation Front (NSF) said the result had been secured by "fraud, violations and organisational shortcomings".

"The referendum is not the end game. It is only a battle in this long struggle for the future of Egypt," it said. "We will not allow a change to the identity of Egypt or the return of the age of tyranny."

The opposition claims the new constitution will be a catastrophe for political and economic rights in Egypt. Critics say it seeks to enshrine Islamist rule and does not sufficiently protect the rights of women and minority groups.

Opposition concerns over the poll were fuelled by a marked disparity in the results between the first and second round. In the first round, which covered 10 governorates including the capital, Cairo, the result was a marginal victory for the "yes" vote by 54%. This ballooned in the second round to 72%.

Opposition activists alleged there had been violations at polling stations, including inadequate judicial supervision of ballot boxes and attempts by staff to influence voters.

In a statement, the FJP admitted some irregularities had been reported, but said they were so few and so limited that "they had no effect on the integrity of the referendum". Hamdeen Sabahy, NSF member and former presidential candidate, said: "There is no consensus on this constitution. It has split the country and [the low turnout] indicates it is not acceptable as the constitution of Egypt."

The unofficial figures showed a turnout of just 32% of Egypt's 52 million registered voters – significantly lower than in June's presidential runoff between Morsi and Hosni Mubarak's last prime minister, Ahmed Shafik.

Opposition groups say the low turnout casts doubt on the legitimacy of the referendum, and Michael W Hanna, a fellow at the Century Foundation thinktank, argued that the result represented a warning of growing political apathy.

Yet the Muslim Brotherhood and opposition parties could also take heart from the result, he added. "For the Islamists, the fact that many Shafik voters stayed home, or perhaps voted 'yes', is a source of encouragement. For non-Islamists, this vote again shows the mobilised Islamist base is perhaps 15% of the total population, [as it was in] the presidential runoff. If non-Islamists can mobilise voters, the Islamist base is not insurmountable."

Liberal politician Amr Hamzawy said: "The majority is not big and the minority is not small," adding that the NSF would use "all peaceful, democratic means" to challenge the constitution.

The runup to the referendum caused increasing polarisation in Egyptian politics, which began in late November when Morsi issued a decree granting him judicial immunity and powers to protect the Islamist-dominated constituent assembly tasked with drafting the constitution.

Protests and violence erupted throughout Egypt, culminating in heavy clashes on 5 December when FJP supporters forcibly dispersed an opposition sit-in at the presidential palace in Cairo. Nine people died.

In this divisive climate, the assembly rushed to finish the draft and Morsi called for the referendum. Among the claims and counterclaims, Brotherhood leaders used sectarian language to attack the opposition, confirmed when the FJP secretary-general, Mohamed El-Beltagy, told the Guardian 60% of protesters at the presidential palace were Coptic Christians. He declined to elaborate on that statement, saying he was stating a fact and not interpreting it.

"The divides and polarisation are here to stay," Hanna said. "The sectarian rhetoric of the 'yes' campaign and by Brotherhood leaders will have long-lasting ramifications. The passage of the constitution is unlikely to usher in any semblance of stability and, in fact, might institutionalise the current political crisis. Of course, these divides make taking serious economic decisions next to impossible, while the economic status quo remains untenable."

"I see more unrest," said Ahmed Said, head of the liberal Free Egyptians party. He warned that anti-Morsi sentiment was growing. "People are not going to accept the way [he is] dealing with the situation."