The apex court granted four weeks time to the Trust to make requisite infrastructural and other changes for compliance of the Bombay High Court order on the issue.
"The Haji Ali Dargah Trust truely believes in complete equality between men and women," the counsel for the Trust told a bench headed by Chief Justice T S Thakur.
Seeking compliance of High Court's order in "letter and spirit", the bench, also comprising Justices D Y Chandrachud and L Nageswara Rao, disposed of the appeal of Dargah Trust saying, "So long as, you (trust) grant access to women as asked by the High Court, we don't have any problem."
Subramanium, however, sought two weeks for making some "logistic" and infrastuctural changes for compliance of the High Court order.
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"We will grant you four weeks time," the bench responded.
The senior lawyer also referred to an additional affidavit and the notification issued by the Trust on October 11 that they were not averse to the entry of women inside the Haji Ali shrine in south Mumbai.
Earlier, the apex court had extended the stay granted by Bombay High Court to facilitate an appeal against its decision to lift the ban on entry of women near the sanctum sanctorum till today.
Subramanium had then assured the bench that he was on a "progressive mission" and said all holy books and scriptures promoted equality and nothing which is regressive in character should be suggested.
The Trust had moved the apex court challenging the High
Court order lifting ban on women from entering the sanctum sanctorum of the renowned Muslim shrine in South Mumbai.
The High Court on August 26 had held that the ban imposed by the Trust on women from entering the sanctum sanctorum of the Haji Ali Dargah, contravened Articles 14, 15 and 25 of the Constitution and said women should be permitted to enter the sanctum sanctorum like men.
It had granted a six-week stay on the order on a request by the Dargah Trust to enable it to appeal before the Supreme Court.
The high court had held that the Trust had no power to alter or modify the mode or manner of religious practices of any individual or any group.
The High Court in its 56-page judgement had also noted that the "right to manage the Trust cannot override the right to practice religion itself".
It had also refused to accept the Trust's justification that the ban was imposed for safety and security of women, in particular, to prevent sexual harassment at places of worship.
The Trust had claimed that the ban was in keeping with an order of the Supreme Court where stringent directions were issued to ensure that there is no sexual harassment to women at places of worship.
The Maharashtra government had earlier told the court that women should be barred from entering the inner sanctorum of Haji Ali Dargah only if it is so enshrined in the Quran.