Gujarat, one of the three beneficiary states of the dam, goes to polls later this year, the other two are--Madhya Pradesh and Maharashtra.
The CPI(M) also alleged that the government drew "wrong" interpretation of the Supreme Court's February 8, 2017 order to lower the dam's gates in Gujarat.
It argued the apex court had "clearly" ordered that the affected people can be removed post July 31 only after they were provided rehabilitation arrangements and proper compensation was offered.
Out of the total 18,063 families affected by the project in Madhya Pradesh, 6,724 continue to live in submergence area, the Centre had said.
More From This Section
Of these, 884 PAFs are in the process of shifting, Minister of state for water resources Sanjeev Kumar Balyan told the Upper House.
He had also said that all the PAFs have been given resettlement and rehabilitation package as per the Narmada Water Dispute Tribunal (NWDT) award and the SC order.
"The CPI(M) demands that until the conditions of rehabilitation and compensation are not met with, no one must be displaced and the gates of the Sardar Sarovar must be kept open," the party Politburo said in a statement.
The CPI(M) also expressed solidarity with social activist Medha Patkar and some project affected people over their on- going protest in Madhya Pradesh against the "forceful displacement" of the locals from submergence area in the state.
The party claimed that the arrangements for the families of the affected have not been completed.