"I am confident that the spirit of mutual respect and understanding will continue to guide our nations to work together for the wellbeing of our peoples," Prof Yunus wrote to PM Modi on June 6.
The interim government on Sunday shared both the letters through its verified social media handle.
He said Eid-ul-Azha is a time of reflection, which brings communities together in the spirit of festivity, sacrifice, generosity and unity and inspires them all to work together for the greater benefits of the peoples across the world.
Prof Yunus said he deeply appreciates PM Modi's thoughtful message, kind greetings and warm wishes on the occasion of Eid-ul-Azha, which reflects the shared values between the two countries.
"I also would like to convey my warmest greetings to you, and through you, to the people of India on this auspicious occasion," the message from Prof Yunus reads.
On this blessed occasion, Prof Yunus wished PM Modi good health and happiness and the people of India peace, progress, and prosperity.
Earlier, on behalf of the people and the Government of India, PM Modi on June 4 conveyed warm greetings to Prof Yunus and the people of Bangladesh on the auspicious occasion of Eid al-Adha, reports UNB.
This holy festival is an integral part of the rich and diverse cultural heritage of India and is celebrated with immense joy and fervour by millions of people of Islamic faith across the country, Modi said.
"It reminds us of the timeless values of sacrifice, compassion and brotherhood, which are essential in building a peaceful and inclusive world," PM Modi mentioned.
"I take this opportunity to extend my best wishes for your good health and well-being," the message from Modi reads.