"At the Russian president's request, the emergencies ministry will send four cargo planes with tents for 5,000 people, construction materials, food and essentials supplies," a source in the ministry said.
The first two planes are scheduled to take off for Cuba on Wednesday.
On Saturday hurricane Gustav swept through Cuba with winds reaching 300 km p/h (186 mph) as it hit the Isla de la Juventud, in the south of the Cuban mainland.
The storm later swept through the province of Pinar del Rio on the country's western tip, damaging around 86,000 houses and leaving much of the region without electricity.
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The clash of Russian and Western interests has given rise to a geopolitical battle. German politicians are trying to leave all doors and windows open for dialogue with Russia. Moscow does acknowledge this, and Germany is probably the only country with which it is ready to discuss European security.