The Mirazh was involved in Russia's "peace enforcement" operation which began after Georgia launched an offensive in breakaway South Ossetia on August 8.
Reportedly, it was the Mirazh that sank a Georgian vessel during an attempted attack on Russian ships near Abkhazia's coast last week.
The vessel was greeted by crowds of people waving Russian flags and fireworks, while a group of students from western Ukraine held banners, which read "Shame" and "Out of here!"
Meanwhile, a high ranking source in the Turkish Naval Forces said that two NATO frigates carrying humanitarian aid for Georgia had entered Black Sea waters.
Speaking Friday at RIA Novosti news conference, the deputy chief of the Russian military's general staff expressed doubts whether it is necessary to have NATO vessels in the Black Sea delivering humanitarian aid to Georgia.
"Now that the conflict [with South Ossetia] is exhausted, there are NATO vessels [in the Black Sea]. What for and with what aim?" Col. Gen. Anatoly Nogovitsyn said.
He also said Russia would reply swiftly to all provocations against its Black Sea Fleet.
"This is a relatively new statement for me. I think all issues, including similar provocations, have been discussed under bilateral agreements between Russia and Ukraine on the status of the Black Sea Fleet. We will give a prompt response if anything happens," Nogovitsyn said.
Ukrainian President Viktor Yushchenko signed a decree last Wednesday requiring prior notification from Russia of all movements by naval vessels and aircraft from the country's Black Sea Fleet base in the Crimea.
Ukraine even threatened to refuse Russian vessels entry to the Sevastopol naval base. Russia's Black Sea Fleet uses the Sevastopol base under agreements signed in 1997. Yushchenko announced earlier this year that Ukraine would not extend the lease beyond 2017.
Reported by RIA Novosti