Ivan Melnikov, who is also a member of Russia's lower house of parliament, said the government's anti-crisis measures "were either ineffective or were carried out in the interests of a small circle of individuals."
Russia has been hard hit by the global financial crunch that was sparked by the subprime mortgage crisis in the United States last summer and quickly spread to the rest of the world. Unemployment is up, and the ruble has lost about 40% of its value. The economic slump has also seen a drastic decline in oil prices, Russia's most important export.
The Communist Party held protests throughout the winter against hikes in utility charges, as well as increasing fuel and food prices.
"The planned protest will differ from all the others," Melnikov said. "For the first time we are demanding that the government resigns."
The Communists earlier called for the resignation of some individual ministers, including Finance Minister Alexei Kudrin and Education Minister Andrei Fursenko.
"Our complaints [against the government] have not just piled up, they are overflowing," the Communist Party press office quoted Melnikov as saying.
According to Melnikov, if the government did not hear the call for individual Cabinet members to step down, then "it's time to change the entire Cabinet."
He also said that the party would strive to make the rallies as large as possible, adding that, "Everyday life is causing more and more people to join our protest."
The Communist Party is the second largest party in the State Duma with 57 seats. The pro-Kremlin ruling United Russia party has 315 seats.
