Two students killed in clashes with police at the Islamic Al-Azhar University in Cairo on Sunday, state news agency MENA reported, quoting university officials.

Egyptian riot police fired buckshot and tear gas at pro-Muslim Brotherhood university students who threw stones at them outside the university, as anti-government student protests continued for a second week.

Protests have intensified over the last week at campuses across Egypt, in the wake of a court ruling handing down death sentences to more than 500 alleged Brotherhood supporters in the city of Minya. A police van was also set on fire outside the gates of the university.

The protesters are demanding the reinstatement of students who have been expelled for taking part in demonstrations or for belonging to the Muslim Brotherhood, and are also protesting against a bid for the presidency by former army chief, Abdel Fattah al-Sisi.

Egypt's electoral authorities announced today that the first round of presidential elections will take place on May 26th and 27th.

Last week a student was killed in similar protests at Cairo University. Egypt's security forces have mounted an intense crackdown on the Muslim Brotherhood since the ousting of Islamist president Mohamed Morsi by the military last July, killing hundreds of its members and jailing thousands of others.

The electoral commission has said that the voting results are to be expected by June 5. If a second round is necessary it will be held by mid-month with results announced no later than June 26, the commission said.

The country's powerful former military chief Abdel-Fattah el-Sissi, who led the overthrow of Islamist President Morsi last summer, has announced his bid for office and is widely expected to win. His victory would restore a tradition of presidents from military backgrounds that Egypt had for all but one year since 1952, when officers overthrew the monarchy and became the dominant force in politics.

A mostly conscript force that fought four wars with Israel, the army has a strong support base among the population, many of whom see it as a pillar of the country's identity.

Morsi was removed from office on July 3, amid massive protests demanding his resignation and accusing him of monopolizing power and mismanagement in the face of myriad economic and social problems. The military, led by el-Sissi, stepped in to remove Morsi and backed a political road map that promised presidential and parliamentary elections.

But the country's division only grew with Morsi's ouster. His backers, largely Islamists and sympathizers, have held near daily protests demanding his reinstatement, describing the military overthrow of Morsi as a coup. Youth groups who initially backed Morsi's ouster have increasingly grown critical of the military's handling of the post-Morsi days, denouncing a heavy crackdown on Islamists and dissent. Several thousands have been detained and killed in political violence.

A police car set on fire by students of Al-Azhar University, who are supporters of the Muslim Brotherhood and deposed President Mohamed Morsi, is seen during clashes with riot police at the university's campus in Cairo's Nasr City district, March 30, 2014. (Amr Abdallah Dalsh/Reuters)

But, with a widely divided opposition, el-Sissi has garnered wide support among a public wary of turmoil.

Although military spokesmen denied for months the military chief was planning to run for office, the 59-year-old el-Sissi finally announced on Wednesday that he was leaving the army to run for office — a requirement since only civilians can run for president — saying he was responding to a popular call.

El-Sissi said he will work to "fight every day for Egypt free of fear and terror." The Brotherhood and allies have said his nomination for office would only increase instability in the country.

To officially make a bid, el-Sissi would have to collect at least 25,000 signatures from 15 out of Egypt's 27 provinces in a petition demanding he runs. He had said he will not run a traditional campaign, most likely over concerns for his own security. So far, only one other candidate, leftist Hamdeen Sabahi, who took third place in 2012 presidential elections, has said he would run.

The commission said that the window for nomination of candidates will open Monday until April 20. A three-week campaign period is slated to start on May 3.

Allegations of espionage

Egypt's interior minister, meanwhile, told reporters that prosecutors were investigating allegations that Morsi's secretary had seized confidential national security documents while he was in office with the intention of passing them on to a foreign espionage agency and the media.

The minister, Mohammed Ibrahim, said his agents seized the documents, smuggled out of the presidential palace, before they were leaked to Qatar-based Al-Jazeera network, and the intelligence agency of an Arab country allied with the Brotherhood. He did not name the country, but he was clearly referring to Qatar. He said Morsi's secretary, Ayman el-Sirafy, was in custody. Ibrahim said el-Sirafy had recently instructed his daughter during a jail visit to hide the documents.

Morsi and senior members of his palace staff are already facing trial on espionage charges, including leaking secret national security documents to foreign militant groups, like Palestinian Hamas and Iran's Revolutionary Guard. Ibrahim, who is in charge of police along with domestic security agencies, did not say whether the new allegations will be added to the ongoing trial or be dealt with separately. If convicted of espionage, Morsi could face the death penalty.

Ibrahim, appointed by Morsi but stayed on after his overthrow, did not reveal the contents of the documents in question, saying only that they filled three large suitcases and that they touched on "everything that you can imagine which affects national security."

He did not provide a sequence or a time frame while presenting details of the allegations, and dodged a question on whether the documents were leaked out of the palace at Morsi's request.