The shrine named after 11th century preacher Sheikh Abdul Qadir Jeelani, popularly called as Dastageer Sahib, at Khanyar in downtown Srinagar was completely destroyed in the fire on June 25.
"We are deeply sorry that such a revered shrine should have been virtually destroyed in fire," Chidambaram told reporters here.
He assured the state government of full support in rebuilding the shrine.
"Both Chief Minister (Omar Abdullah) and Farooq Abdullah (Union Minister) have told me that it is their intention to rebuild the shrine and I have told them that yes government of India will fully support their effort to rebuild the shrine.
"And I think already INTACH (Indian National Trust For Art and Cultural Heritage) has been asked to give a design... help them in rebuilding the shrine," he said.
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Chidambaram said that the central agencies working in the state are cooperating with the state authorities in ascertaining the cause of the fire.
"I think the intelligence agencies present in Srinagar are working with the state government. The cause of the fire is to be established," he said.
Declining to comment further, he said, "It is only investigation that will reveal the cause of fire."