Murad Ali of the Brotherhood's Freedom and Justice Party said that shooting broke out in the early morning while Islamists staged a sit-in outside the Republican Guard barracks.
Muslim Brotherhood spokesman Gehad El-Haddad says hundreds of critically wounded are being taken to hospitals.
Locals on the ground say no warning shots fired before the security forces attacked. Ambulances are at the scene.
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IAEA ex-head to become Egyptian vice-president
Egypt's Social Democratic leader Ziad Bahaa el-Din is to become the new prime minister, while the leader of the liberal opposition, IAEA ex-head Mohammed el-Baradei, will be vice president.
This information was circulated by the Sky News Arabia TV channel with reference to a source in the President's Administration.
Earlier el-Baradei declined the post of prime minister and nominated Ziad Bahaa el-Din instead, RIA Novosti reports.
In the past Ziad Bahaa el-Din, who has a lawyer's and an economist's degrees, headed the Financial Control Division. He is one of the leaders of the Egyptian Social-Democratic Party and is well-known as a fighter against corruption in government agencies. 
Morsi supporters, opponents hold huge rallies in Egypt on Sunday
Opponents and supporters of ousted Egyptian president Mohammed Morsi Sunday held huge rallies in several parts of the country amid fears about new violence between the two sides.
Thousands of Morsi supporters gathered at sites in eastern and southern Cairo, demanding the reinstatement of former Islamist president who was ousted by the army after massive street protests against his rule earlier in the week.
Islamists gathered outside the headquarters of the elite Republican Guard in eastern Cairo, where they believe Morsi is being kept in the army's custody.
Waving Morsi's portraits and the Egyptian flag, they chanted slogans against the engineer of Morsi's toppling, Defence Minister Abdel-Fatah.
Leaders of the Muslim Brotherhood, of which Morsi is a member, have vowed open-ended street protests until he is restored to power, calling his removal a "coup against legitimacy."
Several anti-Morsi marches Sunday converged on Tahrir Square in central Cairo, renewing support for Morsi's overthrow.
"The people have already toppled the regime," chanted the demonstrators.
"The Egyptian army is ours, but Morsi is not," they added, as army helicopters flew overhead.
Hundreds of anti-Morsi demonstrators gathered outside the presidential palace in the eastern Cairo quarter of Heliopolis, renewing backing for his toppling.
The rallies were held in response to a call from the grassroots Tamarod movement - which spearheaded the campaign for Morsi to be unseated - in support of what it called "popular legitimacy."
Tamarod has accused the Brotherhood of planning to "drag the nation into infighting" by insisting on Morsi's reinstatement.
Checkpoints manned by self-styled guards were set up on the entrances to the iconic square to keep assailants at bay.
Rival rallies were also held in Alexandria, Egypt's second biggest city, the Nile Delta province of Beheira and the southern city of Aswan, according to local media.
Clashes on Friday pitting Morsi's supporters against opponents and security forces left 36 dead and more than 1,000 injured, according to health officials.
Three soldiers were injured Sunday when gunmen fired on them in al-Arish, the main city of northern Sinai, said witnesses.
The attack was the latest in a series of assaults targeting army and security personnel in the Sinai Peninsula since Morsi's overthrow.
Suspected radicals had earlier on Sunday blown up in Sinai a pipeline that exports gas to Jordan, a security source said.
The fire from the blast was seen 50 kilometres away, the source said.
Muslim militants have been blamed for attacks on Sinai gas pipelines after the 2011 uprising that forced president Hosny Mubarak from power. Until Sunday, no attacks had been reported since July last year.
Egyptian authorities Sunday took further judicial moves against Brotherhood leaders and allies, with arrest warrants being issued for two more senior leaders of the conservative Islamist group.
State-run newspaper al-Ahram reported online that Brotherhood leaders Essam al-Erian and Mohammed al-Beltagy were to be investigated for incitement to murder over the deaths of protesters as the Brotherhood headquarters in a Cairo suburb came under attack last week.
Prosecutors also ordered 15 days pre-trial detention for firebrand Islamist preacher Hazem Salah Abu Ismail, held since Friday on charges of inciting killing opposition protesters.
Morsi, who won election last year by a narrow margin, is accused by the opposition of putting a priority on tightening the Muslim Brotherhood's hold on power and failing to address the country's problems.
His four-year term was to end in 2016.
 DPA, Reuters, AFP, RT, Omo Oodua Blog