CAIRO, March 30 (Reuters) - An Egyptian soldier was killed on Sunday when militants attacked the bus he was driving in the town of Al-Arish in the Sinai Peninsula, the military said in a statement posted on Facebook.

An army source told Reuters the bus was transporting police officers, three of whom were wounded. There was no immediate claim of responsibility for the attack.

Sinai-based militants have stepped up violence against the state since the army ousted Islamist President Mohamed Mursi of the Muslim Brotherhood in July, killing more than 400 soldiers and police, according to the Foreign Ministry.

The Egyptian army, the biggest in the Arab world, has launched offensives against militants in the Sinai but the operations have failed to reduce the number of attacks on security forces. The violence has spread to the capital Cairo and other cities which also regularly witness demonstrations against the military-backed government.

Security forces clashed later on Sunday with Mursi supporters demonstrating at the campus of Al-Azhar University, a common site of unrest in recent months.

A Reuters witness said police used tear gas and buckshot to disperse the protesters who had attempted to block traffic in the main street outside the university.

Security forces have mounted a tough crackdown on the Muslim Brotherhood, killing hundreds of its members and jailing thousands of others.

(Reporting by Stephen Kalin and Yasmine Saleh; Editing by Michael Georgy and Mark Heinrich)