Terming India an "old and tested friend" since 1971, Inu said the meeting was with an old friend Shringla.
He said relationship between Bangladesh and India are getting deeper under the current government and termed the visit "meaningful."
Talking to media after the meeting at a city hotel, he said many cooperation efforts are going on between the two countries amid COVID-19 pandemic.
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Inu referred to the virtual meeting of Saarc leaders and said the two countries are working for the development of South Asia.
Shringla, who served as Indian High Commissioner to Bangladesh, assumed office of the Indian Foreign Secretary in January this year.
As the Foreign Secretary, he first visited Dhaka in March this year.
He is currently on a visit to Dhaka to discuss and "take forward cooperation" on matters of mutual interest, said the Indian HighCommission in Dhaka soon after his arrival on Tuesday.
He is scheduled to leave Dhaka today (Wednesday) after his meeting with Bangladesh Foreign Secretary Masud Bin Momen.