The Akula class nuclear attack submarine on a ten year lease to the Indian Navy left its base on the Pacific coast earlier this week, bound for India, RIA Novosti and Interfax news agencies reported.
With the expected induction of Nerpa by year-end, it will be after 19 years that the Indian Navy would have a nuclear submarine in its fleet.
India's indigenous nuclear submarine INS Arihant is presently undergoing sea test trials.
However, an official of the shipyard said that the submarine was still undergoing final sea trials. The Russian Navy's Pacific Command refused to comment.
Reports said that the Nerpa submarine which has been re-christened INS Chakra leased at a cost of USD 650 million is accompanied by Russian instructors, who will help Indian naval crew to bring it to the new port of deployment.
"The Nerpa has not been yet handed over to the Indian Navy," an official of the Amur Shipyard in Russia's far eastern Khabarovsk region said over phone.
"Presently the joint Indian-Russian naval crew is completing the combat training on the high seas," the shipyard official added.
But experts here do not rule out that the Russian Navy wants to formally hand over Nerpa to the Indian Navy on the Indian coast and the so-called training mission could be a cover for security reasons.
The submarine has been handed over two years after an accident onboard during testing killed 20 people. The Amur shipyard, the builders of the sub said the vessel was now completely retrofitted after the November 2008 accident
Russia's Akula-II class submarine is considered to be the quietest nuclear submarine and during its trials by the Russian Navy since January its acoustic noises have been further reduced by the Amur Shipyard, which was initially to deliver the submarine in 2007.