The court also asked the Maharashtra government to decide within a week the plea seeking regularisation of the mosque.
A bench comprising Chief Justice J S Khehar and Justice DY Chandrachud took on record the consent of all parties including the Haji Ali Trust that if the state government rejects the regularisation plea, nobody will oppose the demolition of portions of the mosque which are built on encroached land near the historic shrine.
It has been alleged that certain part of the Kinara mosque falls under the encroached area which have been ordered to be cleared by the Bombay High Court. The Supreme Court has also upheld it.
The bench has now fixed the matter after one week.
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The apex court had earlier given a last opportunity to the Maharashtra government and warned it of serious consequences if squatters from 908 square metre area near the historic shrine were not removed in two weeks.
It had made it clear that the encroachments have to be removed within two weeks from July 3 from the 908 square metre area earmarked in the Bombay High Court order.
The HADT had on April 13 agreed to remove encroachments on its own by May 8 and was later given some more time to remove the squatters.
The trust's offer to remove and demolish the encroachments had come after the apex court made it clear that only the mosque, located on an area of around 171 sq metres, would remain protected while the rest of the area, measuring 908 sq metres, has to be cleared of squatters.
The Haji Ali Dargah was constructed in 1431 in the memory of a wealthy Muslim merchant, Sayyed Peer Haji Ali Shah Bukhari, who gave up all his possessions before making a pilgrimage to Mecca.
The High Court had ordered the formation of a joint task force comprising the Municipal Corporation of Greater Mumbai and the Collector to remove the illegal encroachments on the approach road leading to the Haji Ali Dargah.
The High Court was hearing a petition filed by Sahayak, a socio-legal and educational forum, seeking immediate removal of the encroachments on the approach road to the dargah which is located on the sea.