CAIRO – Egypt’s main opposition bloc on Sunday alleged widespread fraud and called for mass protests after preliminary results showed supporters of a controversial draft constitution winning a solid majority in the first round of balloting.

The call had the potential to throw Egypt back into disarray after several days of relative calm that included orderly voting Saturday by about 8 million citizens. Preliminary tallies by the Muslim Brotherhood and state media showed that 57 percent of voters backed the constitution, with a second round of voting still to come. Many of those who voted for the charter said they were doing so to restore stability to the country after nearly two years of tumult that began with a successful push to oust President Hosni Mubarak.

But in a Sunday night news conference, the opposition National Salvation Front alleged there had been thousands of complaints of voting irregularities that “went beyond the rigging that used to take place under the previous regime.”

The group, a loose coalition of liberals, leftists and Christians that has emerged to challenge the ruling Islamists, called on Egyptians to protest Tuesday “in order to defend their free will and to prevent any rigging of their decisions.”

The opposition’s reaction to its apparent defeat seemed to end any hopes that the referendum might bring calm to Egypt after weeks of clashes over both the substance of the new constitution and the hurried way it was put before voters.

The unofficial results of the first round reflected a narrower-than-expected victory for the charter, which was strongly backed by President Mohamed Morsi and his allies in the Muslim Brotherhood. Wider margins are forecast Saturday during the second round of balloting, when voting shifts to smaller cities and more rural areas, where Islamists have a clear edge.