A bench of Acting Chief Justice Gita Mittal and Justice C Hari Shankar said the authorities needed to look into the matter and take a view "expeditiously".
"The respondents (Centre and the ministries concerned) need to examine and take a view thereafter expeditiously. The decision should be communicated to the petitioner (advocate)," the bench said.
It added, "We are of the view that it should be looked into as it was an important matter".
The plea referred to a recent notification of the Centre, scrapping a subsidy for cheaper flights for the pilgrimage.
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Since the subsidy had now been scrapped, it said there was no need for a government-controlled panel to manage its affairs and the Haj Committee Act 2002 was also liable to be quashed.
The central government had in 1959 introduced a subsidy for air travel between Bombay and Jeddah. Other flights on Air India, the state-owned carrier, were added over time.
It pointed out that the Sikh community in India was allowed to set up its own body to manage its minority affairs under the Sikh Gurudwara Act, 1925.
The question of whether the government should continue to look at the affairs of the Haj Committee, right from inviting applications for Haj till the return of Hajis after the pilgrimage, had acquired importance after the Centre scrapped the subsidy, the petition said.
The plea has also sought direction to the Ministry of Civil Aviation to either float open tenders inviting bids from all existing airlines flying between India and Saudi Arabia or allowing pilgrims to directly purchase tickets for their Haj flights.
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