Police have killed two demonstrators and arrested 54 others during protests held across Egypt against the military-backed government, the country's Interior Ministry says.

Sixteen other demonstrators were also reported injured, as Egyptian security forces used tear gas to disperse the demonstrations on Friday.

The first protester was shot and killed by birdshot during clashes between anti-coup protesters and police in the canal city of Suez. The second protester was killed during a confrontation between the demonstrators on the one hand, and supporters of the military and security forces on the other, in the town of Fayoum, south of Cairo.

Three policemen were reportedly injured during the clashes, as security officials accused protesters of torching a police car in Suez, and destroying another police car in the southern city of Qena.

Tear gas grenades have become standard use against demonstrators in several Cairo districts after protesters took to the streets against the military's removal of former President Mohamed Morsi, Egypt's first democratically elected leader.

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The protests went ahead despite the country being gripped by icy winter weather, resulting in a rare snow over Cairo, and rain elsewhere.

Protesters lobbed petrol bombs at the police in the capital, the security officials said.

Such demonstrations are regarded as illegal, since they do not conform to a new law requiring organisers to give three days notice of a protest and to have it approved by the government.

In Fayoum, two policemen were wounded by buckshot at a protest, sources told the AFP news agency.

The Anti-Coup Alliance has been organising protests demanding that the military-backed government step down ever since Morsi's government was overthrown in July.

Since Morsi's removal by the military after just a year in office, authorities installed by the army have cracked down hard on protesters.

More than 1,000 people, most of them pro-Morsi, have been killed in what Human Rights Watch called the worst violence in Egypt's modern history, and thousands of Islamists and opposition leaders have been arrested.

Source: Al Jazeera and agencies