The State Election Commission (SEC) has sought a stay of the operation of May 8 order, saying it would suffer "irreparable loss and injury".
Anticipating the SEC's move, the state's main opposition CPI(M) and BJP have filed a caveat before the top court saying that no ex-parte orders should be passed.
Caveat is a legal notice to a court or public officer that certain actions may not be taken without informing the person who gave the notice.
A bench of Chief Justice Dipak Misra and Justices A M Khanwilkar and D Y Chandrachud was told by senior advocate Mukul Rohatgi, appearing for BJP's West Bengal unit, that a copy of the SEC's petition be supplied to them.
The CPI(M) has claimed that many of its candidates were prevented from filing nominations by the state's ruling Trinamool Congress.
On May 8, the high court had directed the SEC to accept the nominations of those candidates named by CPI(M) who had filed their papers electronically within the stipulated time before 3 pm on April 23.