But a senior Russian general has accused Nato countries of using humanitarian aid as a "cover" for a build-up of naval forces in the Black Sea.
Al Jazeera's Neave Barker, reporting from Moscow, said that the Russian government considered the presence of the US vessel "very dubious indeed".
"This is a missile cruiser, it has Tomahawk missiles, it has an array of weapons on board ... no doubt this is going to be sending negative signals to the Russian command," he said.
Earlier on Sunday an explosion ripped through a fuel train outside the Georgian town of Gori, severing a vital trade route across the country.
Georgian officials are assessing the damage from the blast, which could potentially disrupt a key trade route for oil exports from Azerbaijan to European markets.
"The railway is vital not just for the Georgian economy but for the economy of neighbouring countries," Lado Gurgenidze, Georgia's prime minister, said.
Shota Utiashvili, a spokesman for Georgia's interior ministry, told Al Jazeera: "The investigators [suspect] ... the Russian forces that left there two days ago left a mine on the railroad."
"About a week ago, on the same railroad a major bridge was exploded by the Russian invaders. And as they have left the area they have left mines," he said.
Later, Utiashvili said it was possible that debris from explosions at a disused munitions dump nearby had hit the train, causing the fire.
Witnesses said that an intense fire was burning sending flames and thick dark smoke high into the air.
Some witnesses also reported seeing Georgian troops removing a large artillery shell that had been jammed under the tracks.
Russia withdrew the bulk of its forces from Georgia on Friday.
Moscow is maintaining some troops in western Georgia as well as around South Ossetia, the breakaway region of the country which Tbilisi attacked on August 7, leading to Russia sending in forces.
Nicolas Sarkozy, the French president, on Saturday called on Russia to further withdraw its forces from roads linking Georgian cities.
Acting as chair of the European Union, Sarkozy "insisted on the importance of a rapid pullout of Russian soldiers present on the Poti-Senaki route," a statement from his office said.
Georgian authorities said that Russian forces were establishing checkpoints at eight locations skirting the breakaway region of South Ossetia and Georgia's main east-west highway.