Sergey Naryshkin, chairman of Russian Parliament Duma, said the two countries also discussed the possibility of a parliamentary forum of BRICS nations.
"Russia is making all efforts and in the SCO summit certain decisions will be taken to ensure India's full fledged membership at the Shanghai Cooperation Organisation," he said.
"We suggested to create a regular forum of BRICS parliamentarians. Whether this form will grow in regular assembly or any other sort of organisation...We will see," he told reporters.
SCO is a grouping founded in 2001 in Shanghai by the leaders of China, Kazakhstan, Kyrgyzstan, Russia, Tajikistan, and Uzbekistan. India is an Observer State in the organisation.
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India had last year submitted a formal application for full membership of the SCO.
Being one of the largest energy consumers in the world, it feels getting the SCO membership will help it participate in major gas and oil exploration projects in Central Asia. The SCO has amongst its members some of the largest energy producers in the world.
India has been an observer at the SCO since 2005 and has generally participated at the ministerial-level at summits of the grouping which focuses mainly on security and economic cooperation in the Eurasian space.
Naryshkin, who is leading a delegation of Russian legislators, said the two countries also discussed procedures practised in both the houses, which can benefit each other.
He also pitched for greater cooperation among India, Russia and China.
"We also discussed Russia, India, China troika which is becoming a factor in international life and ensuring international stability and security.
"Such formats (cooperation between the three) serve as important sense of security in region and once again impossibilty of creating unipolarity in the world.
"Strengthening relations with India, Russia and China strengthens security in the world," Naryshkin said.