In June, India and Pakistan became full-fledged members of the SCO, a China-dominated security grouping which is increasingly seen as a counterweight to NATO.
India is attending the SCO summit in the Russian beach resort city of Sochi as a permanent member for the first time.
"My congratulations to Pakistan for becoming the full member of SCO," Swaraj said while addressing the 16th meeting of Council of SCO heads of governments.
Pakistan Prime Minister Shahid Khaqan Abbasi was also present during the summit.
The ties between India and Pakistan have been badly hit by a range of issues including cross-border terror attacks in India and the sentencing of Indian national Kulbhushan Jadhav to death by a Pakistani military court for alleged spying.
"This meeting has a special significance for India because it is the first meeting of the Council, after India became the full member of the SCO. Furthermore, it is being hosted by our old and trusted friend Russia," she said while addressing the 16th meeting of Council of SCO heads of governments.
India had been an observer at the SCO since 2005.
The SCO was founded at a summit in Shanghai in 2001 by the Presidents of Russia, China, Kyrgyz Republic, Kazakhstan, Tajikistan and Uzbekistan.
India, Iran and Pakistan were admitted as observers at the 2005 Astana Summit. The Tashkent SCO Summit in June 2010 lifted the moratorium on new membership, paving the way for expansion of the grouping.
Now, the SCO has eight member states -- India, Kazakhstan, China, Kyrgyzstan, Pakistan, Russia, Tajikistan and Uzbekistan.
It also has four observer states -- Afghanistan, Belarus, Iran and Mongolia -- and six dialogue partners -- Azerbaijan, Armenia, Cambodia, Nepal, Turkey, and Sri Lanka.
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