More than 300,000 Rohingya have poured into Bangladesh since the latest flare-up in violence on August 25, adding to around 300,000 refugees already living in Bangladesh, close to the border with Myanmar.
"She (Swaraj) called our Prime Minister last night and conveyed her country's solidarity with Bangladesh over the Myanmar refugee issue," Prime Minister Shiekh Hasina deputy press secretary Nazrul Islam told PTI.
Ms Swaraj, he said, told the Bangladesh premier that the crisis by now appeared as an international issue while India was trying to put "pressure bilaterally and multilaterally on Myanmar to stop persecution on ethnic minority Rohingya Muslims" and take back the refugees who fled to Bangladesh.
According to the spokesman, PM Hasina, on the other hand, said Bangladesh was forced to offer refuge to the refugees on humanitarian ground as they fled their home at Myanmar's western Rakhine state to evade atrocities.
He said Ms Hasina explained to Ms Swaraj the helplessness and miseries of the refugees, particularly of the minor children and women, and said Bangladesh is trying to address their basic needs.
"She (Hasina) told Swaraj that Bangladesh required external supports to handle the refugee issue and return them to Myanmar," the spokesman said.
Ms Hasina said her government allocated land for makeshift shelters of the Rohingyas "but, it will certainly create a big problem for Bangladesh if they stay for long".
The premier's spokesman said Indian High Commissioner in Dhaka Harsh Vardhan Shringla was present at the Hasina's Ganabhaban residence when Ms Swaraj called.
Ms Swaraj's call came hours after the external affairs ministry issued a statement expressing India's readiness to provide Bangladesh "any assistance" in tackling the refugee crisis.