During their meeting, Swaraj raised the issue of the killing of Yasir Javed, a businessman from Srinagar who died in Russia's Kazan city last month following an attack on him by a group of local goons, and enquired about the progress of investigation into the case.
Javed was attacked by unknown miscreants in Kazan city on March 3 and died later at a hospital there after remaining in coma for several days.
She also raised the issue of the death of two Indian girl students, who were killed in a fire at a medical university in western Russia.
Pooja Kallur and Krishma Bhonsle, both from Maharashtra, were studying at Smolensk Medical Academy in Russia and lost their lives in a fire accident in February.
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Swaraj also expressed regret over an acid attack on a Russian girl in India recently and said India has ensured treatment for the girl in India as well as in Russia.
Lavrov thanked Swaraj for dealing with the case effectively.
Lavrov, on his part, said both countries should continue to work closely to further expand bilateral ties.
Both sides should continuously review the agreements being signed at the highest level, he told Swaraj.
Lavrov also expressed gratitude to India for its support during Russia's chairmanship of BRICS (Brazil, Russia, India, China and South Africa). He also ensured Swaraj of Russia's full support to India during its presidency of the grouping that began earlier this year.
Swaraj arrived here yesterday to attend the Russia-India-China (RIC) trilateral meeting of their foreign ministers.