Sheikh Hasina also extended her invitation to Congress leader Rahul Gandhi and party's General Secretary Priyanka Gandhi Vadra.
A Congress delegation comprising Sonia Gandhi, former Prime Minister Manmohan Singh, Priyanka Gandhi Vadra and Rajya Sabha MP Anand Sharma met the Bangladesh Prime Minister here on Sunday morning, a day after she met Prime Minister Narendra Modi.
Sonia Gandhi's meeting with Hasina came "especially considering the bond of friendship between the two families", said the statement.
Sheikh Hasina was accompanied by Bangladesh Foreign Minister Abdul Momen, senior ministers and her advisers.
In the meeting, she recalled with gratitude India's support for Bangladesh's liberation and the special bond of friendship that her father and Bangabandhu Sheikh Mujibur Rahman shared with Prime Minister Indira Gandhi, the statement said, adding she also revisited the period after his assassination when she lived in exile in Delhi.
Sonia Gandhi congratulated Sheikh Hasina on winning the 3rd consecutive term as Prime Minister with the people of Bangladesh reaffirming their trust in her leadership and vision, while Manmohan Singh complimented here for the impressive economic growth made by the country and her initiatives that have led to commendable improvement of social indicators, particularly health and education.
"Sheikh Hasina and Sonia Gandhi also referred to the historic relationship between Indian National Congress and Awami League and reaffirmed the commitment of both the parties to strengthen the party to party exchange at leadership level.
"The leaders exchanged views on wide range of subject of mutual interest which included bilateral relations, the issues pertaining to regional and global economy," said the statement.
Hasina, who was on a four-day visit to India, was slated to return home later on Sunday.
( With inputs from IANS )