The Pyotr Veliky arrived in Mormugao on an unofficial visit January 29 after participating in a PASSEX-type naval exercise in the Indian Ocean with the Indian guided-missile destroyer INS Delhi.
Mormugao is the only port on India's western coast that allows visits by nuclear-powered ships.
After the two-day visit, during which supplies of food and water were taken on board, the Russian cruiser headed for the Somali coast to participate in the second stage of the INDRA-2009 joint naval drills with the Indian Navy, which involves practicing joint anti-piracy operations.
The Pyotr Veliky will join up with a task force from Russia's Pacific Fleet, comprising the Admiral Vinogradov, an Udaloy class destroyer, a tugboat and two fuel tankers, which are carrying out anti-piracy patrols in the Gulf of Aden.
The Russian Navy said on Wednesday that the Northern Fleet's Admiral Levchenko destroyer will also participate in the INDRA-2009 exercise.
Pirates have been increasingly active in the waters off Somalia, where over 110 ships were attacked in 2008, with 42 vessels seized and 815 crew members abducted. Up to 20 warships from the navies of at least 10 countries are involved in anti-piracy operations off the coast of the lawless East African nation.
The UN Security Council adopted a resolution last December authorizing countries and multinational organizations involved in tackling piracy to "undertake all necessary measures in Somalia, including in its airspace" to prevent "acts of piracy and armed robbery at sea."