DHAKA, Sept 9 (Reuters) - Police in Bangladesh said on Sunday they had formally charged two Dhaka University academics with instigating violent student protest in August, which posed a serious challenge to the army-backed interim government.

Professor Anwar Hossain, general secretary of the Dhaka University Teachers Association (DUTA), and Professor Harun-ur Rashid, dean of the Social Science Department were detained on Aug. 24, after the protests that started at Dhaka University's 40,000-student campus spread across the country.

Bangladesh has been under a state of emergency since Jan. 11 and the caretaker administration headed by former central bank chief Fakhruddin Ahmed has vowed to eliminate corruption before it hold parliamentary elections around the end of next year.

Authorities clamped a curfew in the capital and five other cities as clashes between students, said by the authorities to being backed by political activists, and security forces led to one death and 300 injuries.

All universities and colleges in the six cities were also shut indefinitely as part of efforts to end the unrest.

"The charges have been filed at a Dhaka court on Sunday against the teachers and 34 other people, mostly students, because evidences say they either instigated the protest or were involved in it," a police officer said.

The protests started at the Dhaka University over the presence of army troops at a campus football match on Aug. 20, when soldiers were reported to have assaulted some students.

It spread across the country, despite a ban on protests imposed in Bangladesh since January when the interim government took charge after weeks of political turmoil.

Authorities have ordered a judicial inquiry into the incidents, which the government felt were partly fuelled by political groups trying to undermine the caretaker administration and force it to withdraw restrictions on political activities.

Many students and some teachers, especially in the universities, belong to rival political camps led by former prime ministers Sheikh Hasina and Begum Khaleda Zia.

Both the ex-PMs and dozens of their followers, including former ministers and two sons of Khaleda, are now in jail facing charges of corruption and abuse of power.

All colleges and some universities reopened on Saturday after the government said the situation on most campuses was now normal.

But the academic council of the Dhaka University decided to keep it shut until Oct. 28, not allowing students to come back before Muslim Eid al-Fitr and Hindu Durga Puja festivals.

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