The Muslim bodies unanimously said that the money in the name of Haj subsidy, which amounted to around Rs 200 crore last year, went to Air India only and that Muslim pilgrims did not get any direct benefit from it.
JIH Secretary General Muhammad Salim Engineer said the "abrupt" withdrawal of subsidy "is bound to increase the overall cost" of performing Haj which will impact many pilgrims from the poor and deprived sections of society.
"A false impression is being created that this subsidy was an appeasement of the Muslim community and a drag on tax payers' money. But the reality is that this subsidy was a payment taken from the Indian Hajis and given to the national carrier Air India, which had a monopoly for ferrying Hajis to Saudi Arabia," Mr Salim said.
"We urge the government to spell out how it plans to permit other airlines to fly Hajis from India given the exorbitant prices Air India charges Indian pilgrims. The government must float a global tender for hiring an airline for Haj," he added.
AIMPLB General Secretary Maulana Wali Rahmani said he could not understand why Air India charged something between Rs 65,000 to over Rs one lakh from Indian Haj pilgrims, depending upon the embarkation point, for return ticket to Jeddah.
"In normal days, the return ticket to Jeddah from Delhi costs something around Rs 35,000 to Rs 40,000. Now, if you book the tickets three months in advance, and in bulk, for close to two lakh people, the cost should ideally come further down," Mr Rahmani said.
"But here is Air India charging many times over. Why? Why doesn't the government go for open tendering?" he added.
JUH President Maulana Syed Qari Mohammed Usman, too, was for competitive bidding among airlines for ferrying the pilgrims.
"The subsidy was being shown as a favour to the Muslims, which is not true. We have been demanding this (open tendering) for years, and especially after the Supreme Court direction to the government in 2012 to withdraw the subsidy, various Muslim organisations made this demand," Maulana Usman said.
"It was time the government implemented it, and we are sure the cost of travel would come down," he added.
When news agency IANS asked Union Minority Affairs Minister Mukhtar Abbas Naqvi after he announced the withdrawal of Haj subsidy on Tuesday, with the government planning to sell its controlling share in Air India, would it continue to enjoy the monopoly over Haj contract, Mr Naqvi said that these modalities will be "worked out at a later stage".