Russia's Marshal Shaposhnikov ASW ship, the French Vendemiaire light monitoring frigate, the U.S. McCampbell Arleigh Burke class guided missile destroyer, and the HMS Kent Type 23 Duke class frigate were to have taken part in the FRUKUS exercise off the Russian coast on August 15-23.
A Pentagon official earlier said the U.S. would stay away from the drill over the South Ossetia-Georgia conflict.
Washington and London have been critical of Moscow's actions during the conflict, which erupted on August 8 when Georgia attacked Tskhinvali, the capital of breakaway South Ossetia.
During the subsequent counter operation to expel Georgian troops from the de facto independent republic and to reinforce Russian peacekeepers, Moscow sent some 10,000 troops and several hundred armored vehicles into the area.
Previously called RUKUS, the exercises were launched in 1988 as a vehicle for dialogue between the Soviet Union, the United Kingdom, and the United States. They involve training scenarios both at sea and ashore.
France formally joined the group in 2003, and the name of the exercises was changed to FRUKUS.
The exercises typically involve around 1,000 personnel from the four countries.
FRUKUS-2007 was held in the North Atlantic with the participation of the Admiral Chabanenko, a guided-missile destroyer from Russia's Northern Fleet.