Communist Party members in St. Petersburg and the surrounding Leningrad Region have demanded that Gorbachev have his Nobel Peace Prize, awarded in 1990, taken away for his statements.
"We will demand that Gorbachev's prize be withdrawn following his calls for vandalism of the architectural ensemble on Red Square," a party statement said.
Earlier on Wednesday, Gorbachev told journalists at a news conference that the removal and burial of the embalmed body of Bolshevik leader Vladimir Lenin was only a question of time.
"We should not do the grave-digging job right now, but we should certainly acknowledge that the mausoleum has lost its importance and that Vladimir Ilyich must be buried," Gorbachev said.
Lenin's body has been on public display in a glass case in a mausoleum on Red Square since his death in 1924. His continuing presence in the symbolic heart of Moscow has been an ongoing source of controversy since the collapse of the Soviet Union in 1991.
Demands to transfer the body of the architect of the 1917 Revolution to a regular cemetery have consistently been countered by Russian Communists, who insist that the tomb on Red Square remain the Soviet leader's final resting place.
Ivan Melnikov, deputy head of the Communist Party, called Gorbachev's statement on Wednesday "an attempt to exert pressure from those who are disturbed by the memories of the great achievements of the Soviet Union."
"Society will not allow this, and neither will we as a party. Politicians who say this do not know the view of the people," he said.
