Terming the incident as "shocking", senior BJP leader Rajnath Singh sought an immediate inquiry into the incident.
"The destruction of the Sufi heritage shrine is simply outrageous and has shocked everybody who believes in peace and harmony," Singh said in a statement here.
"An impartial inquiry must be conducted and the cause behind this unfortunate and shocking incident must be located," he said.
Describing the shrine as a "symbol of peace and harmony", the former BJP president said the government should take steps to ensure that such religious and devotional places are properly protected.
Expressing its dismay over the incident, the Congress unit in Jammu and Kashmir demanded an immediate high-level inquiry to ascertain the cause of the fire and asked the authorities concerned to initiate steps to repair the shrine.
The Jammu and Kashmir Pradesh Congress Committee (JKPCC) also held a meeting here in which Congress leaders expressed shock over the incident.
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Social activists, too, have expressed concern over the incident.
"The government should initiate an immediate probe and if it is found that the fire was caused by arson then those found guilty must be put behind bars," said B L Kapoor, president of Jammu and Kashmir Human Rights Watch.