Swaraj met 68-year-old Megawati, an old friend of India, and discussed efforts to strengtgen bonds between the two countries.
During their conversation, she recalled how the late Biju Patnaik, former Chief Minister of Odisha, gave her name Megawati.
The Indonesian leader told Swaraj that Patnaik had visited Indonesia to meet her father Sukarno when she was born. She said it was raining heavily so Patnaik suggested the name Megawati (daughter of clouds).
"For me Indonesia is India," she told Swaraj.
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Megawati had served as first and only woman president of the predominantly Muslim country from July 23, 2001 to October 20, 2004.
She is the leader of the PDI-P, one of Indonesia's largest political parties. She also took keen interest in India's experience with electronic voting machines.
Swaraj is here to attend the Asian African Conference.
She also attended a civic reception hosted in her honour here where she asked NRIs to join ambitious 'Make In India' programme launched by Prime Minister Narendra Modi and other flagship programmes 'Namami Gange' and 'Clean India'.