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The Egyptian regime has celebrated the 2013 military coup that toppled the country's first freely elected president Mohammad Morsi with a new national holiday.

Egyptian President Abdel Fattah al-Sisi on Thursday described the coup as a "revolution", in remarks on the third anniversary of mass demonstrations that led to Morsi's overthrow.

"[With] this revolution, the Egyptian people have regained their identity and corrected their path, proving to the whole world that their will cannot be broken," Sisi in a speech broadcast on state television.

"The June 30 Revolution confirmed that it is impossible to impose a status quo on the Egyptian people and whoever thinks they can succeed in doing so is delusional," he said, alluding to Morsi's banned Muslim Brotherhood.

He also warned that "terrorism" was trying to obstruct the will of the people as well as their "hopes and aspirations", as the regime's newly-established holiday was marred by a series of deadly attacks.

Thursday's holiday was punctured by violence in the Sinai Peninsula

National holiday

In Cairo, warplanes flew overhead in honour of the holiday as supporters of Sisi held rallies.

	Morsi has been sentenced to death [Getty]

In the ancient southern city of Luxor, hot-air balloons carrying Egyptian flags flew over pharaonic temples and authorities planned a parade along the Nile River.

Thursday's holiday was, however, punctured by violence in the Sinai Peninsula, where Islamic State group [IS] militants killed a Christian priest and two members of the military in separate attacks.

Later on Thursday, six members of the military, including two officers, were killed in a gun battle with smugglers on Egypt's western border with Libya.

Thursday's violence came a day after Sisi urged security forces to prevent anyone from "spoiling" the June 30 occasion.

Millions took to the streets of Cairo and other cities on June 30, 2013, to call for the removal of Islamist president Morsi.

Sisi, then the army chief, gave Morsi a 48-hour ultimatum to respond to "the people's demands" before ordering the military to overthrow and detain him.

His decision to order the removal of Morsi unleashed protests by the president's supporters, and in turn a crackdown in which hundreds of demonstrators were killed.

Sisi was elected president a year later with minimal opposition.

But many of his backers at the time now say the authorities' crackdown against the Muslim Brotherhood has expanded to include any kind of dissent or opposition.

Since Morsi's overthrow, more than 1,000 protesters have been killed in clashes, including more than 600 killed in a single day on August 14 when police dispersed a Cairo protest camp demanding Morsi's reinstatement.

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