The half-an-hour-long meeting at the newly-inaugurated Bangladesh Bhawan was held after its inauguration, a senior official of the Bangladesh High Commission said.
"Although I was not present at the meeting but we can say that bilateral issues were discussed. Issues related to the security and politics of the region were also discussed," Bangladesh Minister of State for Foreign Affairs Mohammed Shahriar Alam told reporters.
Bangladesh and India are on the "same page" with regard to the return of the Rohingya refugees to Myanmar, he said referring to Hasina's comments on the refugees, who are now lodged in Bangladesh.
"Bangladesh is grateful to India because both countries are on the same page - specially the assurances made by Minister of External Affairs Sushma Swaraj after she visited Myanmar. Swaraj had expressed India's views regarding safe and dignified return of the Rohingya refugees," Alam said.
Hasina had in her speech said that Bangladesh was ready to "even share its food" with the large number of Rohingyas who have taken shelter at Cox's Bazar but Myanmar should take them back.
When asked whether Bangladesh is looking for a joint mechanism to tackle the Rohingya issue and put pressure on Myanmar, Alam said there is no such mechanism.
On whether the issue of Teesta water sharing will be discussed in the meeting, Alam said "Our prime minister had said that issues can be solved through discussions. And we have full faith on Prime Minister Narendra Modi ... Track two dialogue is already on regarding this issue."