The Mount Whitney was the first U.S. naval ship to travel to the port since Georgia fought a short war with Russia last month. Poti was bombed by Russian forces and several Georgian ships were sunk.
Harbor master Vakhtang Tavberidze said Friday the ship had anchored just offshore from the port.
U.S. officials said the ship was bringing humanitarian aid for Georgians.
Russia, however, has been extremely wary about the presence of U.S. and NATO ships in the Black Sea region.
U.S. officials in Washington said Russia would be allowed to inspect the Mount Whitney's cargo.
Russia said Friday it planned no military actions in response to the increased presence of the U.S. Navy in the Black Sea.
Foreign Ministry official Andrei Nesterenko made the comments just before the Mount Whitney arrived in Poti.
Earlier, Prime Minister Vladimir Putin openly questioned the presence of NATO and U.S. ships and pledged an unspecified response.
Asked by a reporter about what Russia's response would be, Nesterenko said Friday that international treaties regulate the presence of naval ships in the Black Sea.
He said: "There is no talk of military action."
Earlier, Russia said U.S. aid to Georgia and recentwill encourage Georgia's "aggressive ambitions."
A Russian Foreign Ministry spokesman made the comments Friday as Cheney continued his tour of three ex-Soviet republics including Ukraine, Georgia and Azerbaijan.
President Bush, for his part, is poised to punish Moscow for its invasion of Georgia bybetween the U.S. and Russia.
With relations between the two nations in a nearly Cold Warlike freeze over Russia's actions against its neighbor last month, planning is under way at the White House for the largely symbolic move by Mr. Bush, according to senior administration officials, who spoke on condition of anonymity because the decision was not yet final.