Egypt's army has cautioned that it will intervene next weekend if mass rallies against the president descend into chaos – but stopped short of endorsing either the president or his secular opponents. In one of the military's strongest warnings since it handed over to civilian government a year ago, Abdel Fattah al-Sisi, the defence minister, said he would not allow Egypt to descend into "a dark tunnel of conflict", and called on all political factions to reach consensus in the week before next Sunday's mass rallies against President Mohamed Morsi.

"There is a state of division in society and the continuation of it is a danger to the Egyptian state and there must be consensus among all," Sisi said.

Morsi's opponents plan to organise massive protests on 30 June, the first anniversary of his election – a day that is the subject of frenzied speculation on both the Egyptian streets and in its media. Many claim they will not leave the streets until the fall of Morsi's regime, arguing that for all his talk of democratic legitimacy, he has little respect for wider democratic values. The army has said it will deploy troops on the streets on that day, while the president says he may introduce a state of emergency if, as expected, the protests spark widespread civil unrest.

More than 15 million Egyptians have signed a petition calling for the president's downfall, furious at Morsi's unilateralism and impatient at plummeting living standards. On Saturday, Mohamed ElBaradei – a leader of Egypt's secular opposition – asked Morsi to step down, at a press conference provocatively entitled "After the departure". Wael Ghonim, one of the most prominent activists from the 2011 revolution that toppled Hosni Mubarak, has also called for Morsi to act as a "patriotic Egyptian" and resign.

There has also been widespread anger at the appointment as governor of Luxor of a figure with links to an Islamist terror group. But on Sunday, Adel al-Khayat, who was a member of Gamaa Islamiya, a group whose associates murdered at least 58 tourists in 1997 at a pharaonic temple in Luxor, resigned from the job just days after he was installed.

While al-Khayat's resignation may temper local anger, it will not quell wider fury at President Mohamed Morsi's administration. For Egypt's leftist and liberals, al-Khayat's appointment was just one of many instances in which Morsi – an Islamist – has prioritised his allies at the expense of national unity.

But Morsi can still rely on strong (if falling) support among Islamist sections of society. On Friday, more than 100,000 Egyptians gathered in support of his presidency outside a mosque in east Cairo. Many questioned why Egypt's first democratically elected president should be forced from office three years before the scheduled end of his term.

"Democracy all over the world works in the same way," said Sabry Roushdy, a teacher who had travelled from a northern city, Kafr-el-Sheikh, and a member of Morsi's Freedom and Justice Party. "You come by the ballot box, and you go by the ballot box. It's not right that a section of society should bring him down just because they don't think he is good for the country."

Morsi himself says he has no plans to step down. "When George W Bush had 22% in the ratings, Americans didn't talk about early presidential elections – that's not the way that democracies are run," a presidential source said this week. "It's not about this president and it's not about this regime. If this is established as a precedent, given the degree of polarisation in Egyptian society today, we will not have a stable government for tens of years."

• This article was amended on 24 June 2013 to clarify that Sisi did not say that it was the demonstrations against Morsi that were an attack on the will of the people. His remarks were ambiguous. This was lost during the editing process.