* Brotherhood continues protests despite upped penalties
* Five killed in clashes across Egypt on Friday
* Health ministry says one dead on Saturday
* Police arrest 60 students for possession of weapons: statement (Adds interior ministry and health ministry statements on Al-Azhar protests, other details)
By Maggie Fick
CAIRO, Dec 28 (Reuters) - One student was killed on Saturday when supporters of the Muslim Brotherhood fought with Egyptian police at the Cairo campus of Al-Azhar University, state media reported.
Shaimaa Mounir, a student activist, told Reuters that the dead student was Khaled El-Haddad, a supporter of the Brotherhood that was designated this week as a terrorist organisation by the state.
The violence followed clashes across the country on Friday in which at least five people died.
State-run newspaper Al-Ahram said that security forces on Saturday fired teargas to disperse pro-Brotherhood students who were preventing their classmates from entering university buildings to take exams.
Protesters threw rocks at police and set tyres on fire to counter the teargas. Al-Ahram quoted a health ministry official as saying that one student had been killed and four injured.
Two college buildings caught fire in the violence. State TV broadcast footage of black smoke billowing from the faculty of commerce building and said "terrorist students" had set the agriculture faculty building on fire as well.
Police arrested 60 students for possession of makeshift weapons including petrol bombs, according to an emailed statement from the interior ministry. Calm had been restored, and scheduled exams had begun after the morning clashes.
Al-Azhar, a respected centre of Sunni Islamic learning, has for months been the scene of protests against what the Brotherhood calls a "military coup" that deposed Islamist Mohamed Mursi as president after a year in office.
Supporters of the Brotherhood took to the streets on Friday after the government designated the Islamist group a terrorist organisation - a move that increases the penalties for dissent against the government installed after the army ousted Mursi in July following mass protests against his rule.
The widening crackdown against the movement that was elected into power after the toppling of veteran leader Hosni Mubarak in 2011 has increased tension in a country suffering the worst internal strife of its modern history following Mursi's ousting.
The army-backed government appears bent on clamping down on dissent ahead of a referendum next month on a new constitution, a step that will pave the way for parliamentary and presidential elections.
Thousands of Brotherhood members have been arrested. More than 250 Brotherhood supporters were arrested on Friday alone using the new classification.
Analysts say the government decision points to the influence wielded by hawks in security services. Some officials, including Interior Minister Mohamed Ibrahim, were appointed by Mursi but sided with the army and have been key players in the security crackdown since the Islamist president's ouster.
Human Rights Watch said on Saturday that the government's designation of the Brotherhood as a terrorist group was "politically driven" and intended to end all of the movement's activities.
"By rushing to point the finger at the Brotherhood without investigations or evidence, the government seems motivated solely by its desire to crush a major opposition movement." said Sarah Leah Whitson of the New York-based rights group.
A conservative estimate puts the overall death toll since Mursi's fall at well over 1,500.
The government has not provided evidence linking the Brotherhood to the recent attacks on security forces and state institutions.
Authorities accused the Brotherhood of carrying out a suicide attack on a police station that killed 16 people on Tuesday, though it was claimed by a radical faction based in the Sinai Peninsula.
An adviser to interim president Adli Mansour said in comments published on Saturday that he believed Egypt would not return to a state of emergency even if the violence continued.
Authorities lifted the state of emergency in November, three months after the army enforced the measures amid the bloody turmoil that followed its overthrow of Mursi.
Mustafa Hijazi told London-based Asharq al-Awsat newspaper that the designation of the Brotherhood as a terrorist group was not political. "Instead, it is the use and application of existing laws," he was quoted as saying.
Under the anti-terrorism law dating back to the presidency of Mubarak, those convicted can be jailed for life. Authorities said this week that the movement's leaders could face the death sentence. (Editing by Alison Williams and Alister Doyle)