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 the army to threaten to 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, clashes between supporters and opponents of the new political order killed 49 people, the health ministry said, showing deep divisions that have flared often since the revolt that raised hopes of a stable democracy.

Egyptian authorities make no distinction between militants who operate in the Sinai and the Brotherhood, which renounced violence in the 1970s and has been declared a terrorist group.

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 were on their way back from a holiday when gunmen opened fire on their bus with automatic weapons and rocket-propelled grenades, security sources said. Security sources said earlier that four had been killed.

Security forces in other parts of Egypt are also coming under increasing pressure, raising concerns that Egypt, which has a peace treaty with Israel and controls the Suez Canal, could soon witness a full-blown Islamist insurgency.

A wave of bomb attacks targeting policemen in Cairo killed six people on Friday.

A Sinai-based militant group which said it tried to kill the interior minister last year claimed responsibility for the bombings, according to the SITE monitoring organisation.

Security forces have killed nearly 1,000 Brotherhood members and arrested the group's top leaders. Many Muslim Brotherhood members have been driven underground.

Those members who protested on Saturday against the army-backed government were exposed to live fire in one district of Cairo, security sources said.

The Interior Ministry said in a statement on Sunday that it had arrested 1,079 "rioters" in possession of rifles, petrol bombs, fireworks, and other weapons. It said that a number of policemen were injured in clashes.

Interim President Adly Mansour is expected to address the nation on Sunday on a timetable for elections.

Army chief General Abdel Fattah al-Sisi, who was Mubarak's head of military intelligence, is seen announcing his candidacy for the presidency soon and is likely to win by a landslide.

Sisi's 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 Louise Ireland)