He paid a courtesy call on Hasina at her office on Sunday, her Press Secretary Ihsanul Karim told the media.
Shringla also recalled that India’s External Affairs Minister Sushma Swaraj had promised Hasina's government 'whole-hearted' support in a meeting with Bangladesh State Minister for Foreign Affairs Shahriar Alam in New Delhi last week.
Praising Bangladesh's financial achievements in past seven years, he said the country would succeed in becoming a middle-income country by 2021 and developed country by 2041.
The prime minister asked Shringla to convey her greetings to Indian President Pranab Mukharjee and Prime Minister Narendra Modi.
The Indian High Commission said in a press release later that it would be Shringla's "endeavour to work towards further expanding and strengthening the close and friendly relations that exist between the two neighbours".