"The suggestion given by CJI Khehar, asking the parties concerned in the Ayodhya dispute to settle the matter through talks, is superfluous and unwise," CPI(M) Politburo said in a statement.
There is a "long history" of negotiations for a settlement and all those efforts proved to be "infructuous", it said.
The situation changed in 1992 and there was no scope for further talks as one side had "unilaterally" taken steps to demolish the mosque, it alleged.
It also objected to Khehar asking BJP leader Subramanian Swamy to consult the parties concerned on whether they can hold talks to settle the dispute outside court.
The Politburo said Swamy is not a petitioner in the case and is a "known advocate" of removing the mosque and building the Ram Temple at the spot.
"The judicial process is concerned with who has the title to the land where the Babri Masjid stood. The Supreme Court must adjudicate on this matter before it and discharge its judicial responsibility," the Left party said.
"It is a sensitive and sentimental issue and it's best that it is settled amicably," it had said.
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