* Brotherhood supporter killed in Damietta, second man killed in Minya
* Muslim Brotherhood declared a terrorist group on Wednesday
* Kerry calls Egypt FM, expresses concern
Muslim Brotherhood supporters and police clashed across Egypt on Friday, leaving at least three dead in protests after the army-backed government declared the group a terrorist organisation.
Violence broke out after Friday prayers.
An 18-year-old Brotherhood supporter was shot dead during clashes in the Nile Delta city of Damietta. Another man was killed in Minya, a bastion of Islamist support south of Cairo. A third person was killed in Cairo, the interior ministry said, without giving details.
Meanwhile, security forces detained at least 265 Brotherhood supporters.
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.
Clashes between police and protesters flared in Cairo and at least four other cities on Friday.
Police fired birdshot and tear gas at student protesters at Al-Azhar'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.
Some analysts believe Egypt may face a protracted spell of attacks by Islamist radicals, in addition to 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 northeast Cairo.
The army-backed government has said 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 terrorism laws.
The government has warned that anyone taking part in pro-Brotherhood protests face five years in prison. Jail terms for those accused under the terror law can stretch up to life imprisonment. Brotherhood leaders face the death penalty.
The interior ministry said in a statement that 265 Brotherhood members had been arrested on Friday. Among them were at least 28 women.
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 him. Thousands of Brotherhood members and supporters have been jailed.
In spite of the pressure, the group has continued near-daily protests.
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.