The USS Mount Whitney, which passed through the Bosporus on Wednesday, brought various supplies, including blankets, hygiene kits and baby food to become the first NATO ship to arrive in Poti since the Russian-Georgian conflict.
Two previous ships, the U.S. Coast Guard Cutter Dallas and USS McFaul docked in the Georgian port of Batumi.
The White House announced Thursday a $1 billion economic aid package for war-ravaged Georgia.
The Black Sea Fleet source also said the flagship of the U.S. Sixth Fleet was big enough to carry heavy weapons, which - the Russian military believes - is probably the main part of the delivery.
An intelligence source said Russia was scrutinizing the vessel. "Very soon it will be clear, what the ship has really brought to Georgia," the source said.
The Blue Ridge class ship is a command and control vessel, which, the source said, coordinates the group of NATO ships in the Black Sea also including two U.S., one Spanish, one German and one Polish vessel.
Lt. Col. John Dorrian, a spokesman for the US European Command, said Friday that Russian peacekeepers would not be allowed to examine the cargo as the port of Poti is on sovereign Georgian territory.
Russia's Foreign Ministry said Friday that the overall deadweight of NATO ships can exceed the limit set by international agreements and added that no military action is planned against the vessels.
The U.S. aid is being provided to Georgia after it launched an assault on South Ossetia in an attempt to regain control over the republic, which split from Tbilisi in the early 1990s.
Moscow subsequently launched an operation to "force Georgia to accept peace," which was concluded on August 12. Since then more than 400 metric tons of U.S. aid has been shipped and flown to Georgia amid disputes over the NATO presence in the Black Sea and Moscow's recognition of the independence of South Ossetia and Abkhazia, a second separatist Georgian republic.