(Adds helicopter crash, election announcement)
By Maggie Fick
CAIRO, Jan 26 (Reuters) - Gunmen killed three Egyptian soldiers in an attack on a bus in the Sinai Peninsula on Sunday, the military said, prompting a warning from the army that it would eliminate the Muslim Brotherhood, which it blames for much of Egypt's political violence.
Al Qaeda-inspired Islamist militant groups based in Sinai have stepped up attacks on security forces since the army toppled President Mohamed Mursi of the Brotherhood in July following mass protests against his rule.
On Saturday, the third anniversary of the uprising that toppled autocrat Hosni Mubarak, 49 people were killed in anti-government protests which were attacked by supporters of the new political order and security forces, witnesses said.
Security forces fired live rounds on Brotherhood supporters as they tried to set up a sit-in Cairo's Alf Maskan district, security sources said.
The sources said that 23 people died in the incident, 22 from by bullet wounds, and that they were included in the official death toll of 49.
The violence showed deep divisions that have flared often since the 2011 revolt that raised hopes of a stable democracy.
In another attack in lawless Sinai, five soldiers were killed on Saturday when an army helicopter crashed in the north of the peninsula in an operation against militants. Security sources said it was a missile attack, without giving further details. The army has not commented on the cause of the crash.
Militant group Ansar Bayt al-Maqdis (Supporters of Jerusalem) claimed responsibility for a rocket attack on an army helicopter in a statement posted on the internet. The group also said it was behind a wave of bomb attacks in Cairo on Friday which killed at least six people.
Egyptian authorities make no distinction between militants operating in the Sinai and the Brotherhood, which renounced violence in the 1970s but has been declared a terrorist group by the Egyptian government.
In a statement on Facebook, the army said: "We assure the Egyptian people of the great determination of its men to fight black terrorism and the complete elimination of the advocates of oppression and sedition and blasphemy from followers of the Muslim Brotherhood."
The soldiers who were killed in the bus attack were on their way back from holiday when gunmen opened fire with automatic weapons and rocket-propelled grenades, security sources said.
Security forces have killed up to 1,000 Muslim Brotherhood supporters and put the movement's top leaders in jail. But the tough measures have failed to pacify Egypt, which is of great strategic importance because of its peace treaty with Israel and control over the Suez Canal.
Interim President Adly Mansour announced on Sunday that Egypt's presidential elections would be held before parliamentary polls.
The new political timetable could see army chief General Abdel Fattah al-Sisi, who toppled Egypt's first democratically-elected president, become head of state within months.
Parliamentary elections were supposed to happen first under the roadmap agreed after the army deposed Mursi.
But critics argued that a presidential poll should be held first to elect a strong leader able to stabilise Egypt before potentially divisive parliamentary elections.
Sisi, who was Mubarak's head of military intelligence, is expected to announce his candidacy for the presidency soon and is likely to win by a landslide.
His supporters view him as a decisive figure who can pacify Egypt. The Brotherhood accuses him of masterminding a coup and holds him responsible for what it says are widespread human rights abuses. (Additional reporting by Yusri Mohamed in Ismailia; Editing by Michael Georgy and Rosalind Russell)
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