The second unit generates 1,000 MW of power and the new units will each have the same capacity.
A joint statement issued after the talks said Russia strongly supported India's early entry into the Nuclear Suppliers Group (NSG) and welcomed India's accession to the Hague Code of Conduct against Ballistic Missile Proliferation and the Missile Technology Control Regime.
Unit two was dedicated and foundation of two more units of the Kudankulum plant was laid which was witnessed by Modi and Putin through video conferening.
"Russia is convinced that India's participation will strengthen the international export control regimes and in this regard welcomed India's application for membership in the NSG, reiterating its strong support for India's early entry into the NSG," said the statement.
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"And, with proposed construction of another eight reactors, our wide ranging cooperation in nuclear energy is set to bring rich dividends for both of us. It also fits in with our needs of energy security, access to high technology and greater localisation and manufacturing in India," he said.
On August 10, the first unit of the Kudankulam Nuclear plant was dedicated to the nation jointly by Modi and Putin who had participated at the ceremony from Moscow via video-conferencing.
It said the two sides reaffirm their intention to further expand cooperation under the 'Strategic Vision to Strengthen Cooperation in the Peaceful Uses of Atomic Energy' signed on December 11, 2014.
"In this context they noted with satisfaction a series of positive developments marked in their civil nuclear cooperation this year, including attainment of full power capacity of Kudankulam Unit 1, integration with electricity grid of Kudankulam Unit 2, commencement of the site work for Kudankulam Units 3 and 4," it said.
being made in the implementation of the "Programme of Action for Localisation" between Russia's Rosatom and India's Department of Atomic Energy.
The localisation programme will have active engagement of Indian nuclear manufacturing industry for local manufacturing of equipment and components for upcoming and future Russian-designed nuclear power projects.
Both the sides also noted with satisfaction continued senior official level interactions between their atomic energy establishments, including under the framework of three Joint Working Groups on Nuclear Fuel, Science and Technology and Nuclear Power, and the Central Working Group on Localisation set up during the last two summits.
"A responsible approach to disarmament and non-proliferation is demonstrated by India and Russia's constructive participation in relevant international fora such as the Conference on Disarmament, the Organization for the Prohibition of Chemical Weapons, etc.
"Both sides reiterated their desire to strengthen interaction and coordination of views on these issues," it said.
Russia also supported India's interest in full membership in the Wasseanaar Arrangement, a prominent multilateral export control regime.
The joint statement said the two countries reaffirmed their continued commitment to work together towards development of energy efficiency and renewable energy sources.