"The purpose of the Black Sea Fleet vessels' presence in this region is to provide aid to refugees," the source in the Russian Navy's headquarters told RIA Novosti.
The move comes on the third day of fighting between Georgian and Russian troops in Georgia's breakaway republic of South Ossetia.
The source said the Moskva, accompanied by a patrol vessel and supply ships, travelled from the Russian naval base at Sevastopol in Ukraine's Crimea. The ships will join three large landing craft that earlier arrived in the area from Sevastopol and the Russian port of Novorossiysk.
The source denied media reports saying the Russian fleet's warships were blockading the Georgian coast.
"These reports are not true. A blockade of the coastline would mean war with Georgia, and we are not in a state of war with Georgia."
A spokesman for the president of Georgia's other breakaway republic, Abkhazia, earlier said the local administration and peacekeepers had asked Russia to reinforce its naval presence near the Abkhazian coast after Georgian warships attempted to approach the coastline.
Georgia launched a major ground and air offensive to seize control of South Ossetia on Friday, prompting Russia to send in tanks and hundreds of troops. Georgia imposed martial law on Saturday after Russian warplanes began bombarding military bases.
South Ossetia's capital Tskhinvali has been largely destroyed, and around 2,000 civilians have died according to local and Russian officials. Around 34,000 South Ossetians have fled across the Russian border.
Georgia's leadership began talks on Sunday with the Russian military on creating a humanitarian corridor to allow residents of South Ossetia to escape the ongoing conflict, Reintegration Minister Temur Yakobashvili said.