Swaraj and Meredov, co-chairing the sixth meeting of the inter-government commission, felt that there was scope for both countries to expand cooperation in a number of areas, including energy and education.
Officials said the two leaders resolved to work towards exploring untapped opportunities.
In the meeting, Meredov handed Swaraj congratulatory message from the Turkmenistan President to President Ram Nath Kovind and Prime Minister Narendra Modi.
Meredov also met Defence Minister Arun Jaitley and discussed possible cooperation in areas of defence and security.