The celebrities, including chef Ritu Dalmia, hotelier Aman Nath and dancer N S Johar, have sought protection of their sexual rights on the ground that it is an integral part of the fundamental right to life.
The plea is likely to come up for consideration on June 29 when the court reopens after summer break.
The gay celebrities, in their plea, said their lives have been "inexorably constricted and their rights infringed" by the penal provision.
Earlier, a Supreme Court bench headed by Chief Justice T S Thakur had agreed to hear in an open court the curative plea of NGO 'Naz Foundation' and some gay rights activists.
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On February 2, the court referred the curative plea to a five-judge Constitution Bench for re-examination of the 2-year old verdict by which a colonial law, criminalising consensual sexual acts between the same sex under section 377 of IPC, was restored.
Now, the gay celebrities have filed a fresh writ petition to quash the penal provision.
The apex court had earlier dismissed a batch of review
petitions filed by the Centre and gay rights activists against its December 2013 verdict declaring gay sex an offence punishable up to life imprisonment.
The court had said it did not see any reason to interfere with the December 11, 2013 verdict. It had also rejected the plea for oral hearing on the review petitions which are normally decided by judges in chamber without giving an opportunity to parties to present their views.
While setting aside the July 2, 2009 verdict of Delhi High Court, the apex court had held that Section 377 of IPC does not suffer from the vice of unconstitutionality and that the declaration made by the high court was legally unsustainable.