The Cooperative Longbow/Cooperative Lancer 2009 command-and-staff exercise, which Moscow has criticized as unhelpful in the wake of last summer's armed conflict between Russia and Georgia over South Ossetia, starts on Wednesday and runs until June 1.
Sergei Abeltsev from the Liberal Democratic Party proposed holding "large-scale drills" with the participation of the armed forces of Russia, Cuba and Venezuela in the Caribbean on July 2.
"So that our U.S. partners do not question our peaceful intentions, [I propose] holding the exercises under the codename of 'Reset-2009'," Abeltsev said.
The new U.S. administration recently stated its desire to "reset" relations with Moscow.
He also said the decision to hold the drills in Georgia during WWII Victory Day celebrations was a "total revision of the history of the Great Patriotic War" and a direct insult to Moscow that bordered on a "malicious humiliation."
According to NATO, the drills in Georgia are aimed at improving interoperability between NATO and partner countries, within the framework of Partnership for Peace, Mediterranean Dialogue and Istanbul Cooperation Initiative programs, and will not involve any light or heavy weaponry. Russia was invited to take part in the exercises, but declined the opportunity.
Over 1,300 troops from 19 NATO member or ally states were originally scheduled to participate, but Kazakhstan, Latvia, Estonia, Moldova, Serbia and Armenia have already withdrawn.