A spokesman for the state government told the BBC that the killing of the Buddhist monks was not related to the blasphemy of the Koran.
The shooting followed three days of tension between the local Muslim and Buddhist community over alleged anti-Islamic remarks made by a Buddhist leader.
Orders to shoot at sight were have now been issued in Leh, the capital of the Buddhist-dominated Ladakh district.
Row over remarks
Tension rose in the region after a local Buddhist leader, Sonam Gambo, was reported to have made a derogatory remark against the Muslim holy book, the Koran on Monday.
Local Muslims took to the streets in protest and demanded an apology.
Mr Gambo was arrested and the state's Finance Minister, Abdul Rahim Rather, was sent to Leh to ease the tension.
A spokesman for the state government told the BBC that the killing of the Buddhist monks was not related to the blasphemy of the Koran.
He said they suspected that the monks were killed by separatist militants.
However, the BBC's Srinagar correspondent says Ladakh has been largely unaffected by the decade long separatist violence in Kashmir.
A local Buddhist leader told French news agency, AFP, that the attack on the monks was in reaction to the remarks made on Monday.
"The state administration has failed to protect the minorities in Kashmir, and we are demanding that all our monasteries be secured against attack," the leader, Tsering Samphel, said.
As many as 12 people belonging to both the Muslim and Buddhist communities have been detained.
Strike
Meanwhile, a strike called by an alliance of Kashmiri separatists has closed down shops and businesses in Srinagar, the capital of Indian administered Kashmir.
The strike marks the anniversary of an uprising against the Hindu ruler of the Kashmir state on July 13, 1931, during which Kashmiris were shot dead by police.
A prominent separatist leader, Shabir Shah, was detained when he tried to take out a procession to mark the day.