By Maggie Fick

CAIRO (Reuters) - Muslim Brotherhood supporters and police clashed across Egypt on Friday, leaving at least four dead in protests after the army-backed government declared the group a terrorist organisation.

The violence broke out after Friday prayers and the health ministry said 87 people were wounded in the clashes, which flared in Cairo and at least four other cities.

An 18-year-old Brotherhood supporter was shot dead in the Nile Delta city of Damietta. A second man was killed in Minya, a bastion of Islamist support south of Cairo, and a third person was killed in the capital, the interior ministry said, without providing further details.

A young man was killed late on Friday, the state news agency reported, after clashes broke out in the southern city of Aswan between security forces firing tear gas and Brotherhood supporters who burned two police cars.

Security forces detained at least 265 Brotherhood supporters nationwide, including at least 28 women, the ministry also said.

The widening crackdown has increased tensions in a country suffering the worst internal strife of its modern history since the army deposed Islamist President Mohamed Mursi in July.

Security forces have killed hundreds of his supporters and lethal attacks on soldiers and police have become commonplace.

The Brotherhood was declared a terrorist organisation after 16 people were killed in a suicide attack on a police station on Tuesday, although the group condemned the attack and it was claimed by a radical faction based in the Sinai Peninsula.

The Muslim Brotherhood and its Islamist allies had called for protests in response to the government decision.

GUNFIRE

Police fired birdshot and tear gas at student protesters at Al-Azhar university's Cairo campus. Gunfire was heard in the Suez Canal city of Ismailia, where demonstrators threw fireworks and rocks at police who used teargas, a Reuters witness said.

A number of police officers were injured in the clashes, the interior ministry said. A senior police officer in the city of Minya was injured during clashes between police and demonstrators that began when Brotherhood supporters threw stones at a local police station and attempted to break in, state-run newspaper Al-Ahram reported.

Some analysts say Egypt faces a protracted spell of attacks by Islamist radicals as well as eruptions of civil strife.

A student supporter of the Brotherhood was killed late on Thursday in what the interior ministry described as a melee between supporters and opponents of the Brotherhood in Cairo.

On Friday, a furniture store was set on fire by residents of a Cairo suburb after police stormed inside and arrested three employees, having received complaints that the men had firearms and were Brotherhood members.

The government has said the violence will not derail a political transition plan whose next step is a mid-January referendum on a new constitution.

Officials have issued a new round of harsher warnings against anyone taking part in protests in support of the Brotherhood, saying they will be punished under anti-terrorism laws that envisage five years imprisonment.

Jail terms for those convicted under the terrorism law can stretch up to life imprisonment and Brotherhood leaders face the death penalty.

U.S. Secretary of State John Kerry called Egyptian Foreign Minister Nabil Fahmy on Thursday and "expressed concern" about the terrorist designation of the Muslim Brotherhood and recent detentions, the State Department said.

The Brotherhood, which won every election since Hosni Mubarak was toppled in 2011, has been driven underground since the army deposed the freely elected Mursi in July.

Thousands of Brotherhood members and supporters have since been jailed. Mursi and other top leaders are also behind bars. Despite the pressure, the Brotherhood has continued near-daily protests against the Egyptian authorities.

In a statement condemning the government's freezing of the funds of Islamist charity groups, the Brotherhood accused the government of spreading Christianity by empowering Coptic Christian charities over Islamic ones. (Additional reporting by Reuters TV in Cairo and Yousri Mohamed in Ismailia; Editing by Tom Perry and Mark Trevelyan)