Hours after the incident, Jammu and Kashmir Chief Minister Mehbooba Mufti visited the shrine to assess the damage, they said.
The shrine was built in the memory of renowned Sufi saint Mir Syed Ali Hamdan.
The incident took place around 1 am, the officials of Fire and Emergency Department said adding 22 fire tenders along with pumps were dispatched to the spot immediately to douse the flames.
The fire was brought under control with the help of locals, but by then it had damaged the spire of the shrine, the officials said, adding timely intervention saved the shrine from further damage.
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The chief minister went around the shrine complex to assess the quantum of damage, the spokesman said, adding she sought a detailed appraisal from the local administration of the fire incident.
Mehbooba, who also interacted with the members of the management committee and devotees, said the shrine symbolises the pluralistic ethos of Kashmir society from which every citizen of the state draws spiritual solace.
She also appreciated the local youth who came forward and prevented the fire from spreading, the spokesman said.
The cause of the fire is being ascertained, the officials added.
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