Azad, a former Chief Minister of the state, visited the 200-year-old shrine at Khanyar in downtown Srinagar and assessed the damage caused by the fire, official sources said.
Later, Singh also visited the shrine, the sources said.
They said the two senior Congress leaders were briefed by the management of the shrine and were told that the holy relics enshrined there had been safely retrieved.
Both the leaders expressed satisfaction over the retrieval of the holy relics and assured the management of all possible help in reconstruction of the shrine, the sources said.
Chief Minister Omar Abdullah, who cut short his trip to London, visited the shrine yesterday for a first hand assessment of the damage.
The Chief Minister, who is also the chairman of the Muslim Waqf Board which runs the affairs of most of the shrines in the state, said Dastageer Sahib would be reconstructed as per its old design and architecture.
Meanwhile, life across Kashmir Valley remained disrupted for the third day today due to a strike called by separatists over the incident, even as authorities imposed restrictions on movement of people in the old city.