Indian paramilitary forces Thursday shot dead six people protesting at an incident involving the troops at an Islamic school in Kashmir, police said.

Border Security Force (BSF) troops fired on demonstrators who had gathered outside their headquarters in the district of Gool, two officers said on condition of anonymity.

"It is mayhem. Six are dead and dozens injured. The death toll could rise further," said one officer.

India's Home Minister Sushil Kumar Shinde said he has ordered an investigation into the shooting and appealed for calm in the tense Himalayan region.

A revolt against Indian rule has simmered for decades in Kashmir, the country's only Muslim-majority state.

"I have ordered an inquiry to be conducted without any loss of time to ascertain the circumstances leading to the firing," Shinde said in a statement.

"I assure that any use of excessive force or irresponsible action shall be dealt with strictly," he said.

"The loss of life in this incident is particularly saddening," the minister said, without confirming the number killed.

Protesters clashed with troops after an incident on Wednesday evening at the madrasa (Islamic school) attached to a mosque in Gool, witnesses said.

The head of the madrasa, Qari Shabir, said four BSF troopers came in looking for militants, at the same time that a caretaker was alone there reciting prayers for the Muslim holy month of Ramadan.

"They beat him up...that is when Abdul Lateef (the caretaker) raised an alarm and people started to assemble and the word spread," Shabir told AFP by telephone from Gool, 230 kilometres (143 miles) south of the state's main city of Srinagar.

Other local residents said the troops had entered the mosque to complain about the loud recitation of prayers by worshippers during Ramadan.

The angry protesters clashed outside the BSF base on Thursday with troops who started firing, witnesses said.

"The BSF soldiers fired indiscriminately, downing protesters left, right and centre," one witness who declined to be identified told AFP by telephone.

The insurgency has been a regular source of tensions between residents and security forces, which often spill over into violence.

About a dozen rebel groups have been fighting Indian forces in Kashmir since 1989, either for independence or for a merger with Pakistan. The fighting has left tens of thousands, mostly civilians, dead.

Nuclear-armed rivals India and Pakistan have each administered part of Kashmir since the partition of the subcontinent after the end of British rule in 1947.

Each country claims the territory in full.