They said "by virtue of shared history, geography and culture, people of both Bangladesh and India have bondage of hearts and minds. We have expanded the horizon of our relations manifold in the recent past and would continue to do so in the days to come".
They hoped "that under your able direction the Bangladesh-India relations would grow further".
Hasina also expressed happiness over Mukherjee becoming the first Bengali to hold the highest office of India.
She said "well-deserved election of Pranab Mukherjee as the President of India bears the testimony to trust and confidence which the political leadership and the people of India reposes in him. It's also the recognition of vast experience and knowledge that you have gained over the last 50 years in your politics for the people".
Bangladesh foreign minister Dipu Moni also felicitated Mukherjee and said "we have a common future and I am confident that your statesmanship will enable India and Bangladesh to achieve the fullest potential of our special relationship".
Bangladesh foreign secretary Mirajul Qayes travels to New Delhi on Monday for annual Foreign Office consultations during which the two sides will discuss the entire gamut of bilateral relations.