They issued separate messages on the occasion of Durga Puja on Thursday night, reports BSS.
President Abdul Hamid in his message said: "Religions are of communities but festivals are universal.
"Durga Puja is the major religious festival of Bangali Hindu community. Hindus worship Durga to establish peace in the society through the elimination of demons, ill forces and injustice from the society."
He added: "Durga Puja and other rituals are performed from the depth of traditional heritage and Bangali culture so that the festival is never confined into the circumference of religion.
The president said Bangladesh is a unique example of communal harmony in the world and hoped it would inspire all to contribute better to national development.
"We all hope that the Sharadiya Durgotsab will further consolidate the bonds of friendship and fraternity among the religious communities."
In another message, Prime Minister Sheikh Hasina said Durga Puja is not only a festival of Hindus but of all communities, irrespective of religion.
She mentioned that the main theme of Durga Puja is the victory of good over evil and prayer for truth and beauty.
Bangladesh is a safe abode for people of all religious persuasions. "Our constitution ensures equal rights of the people of all faiths, irrespective of color, creed or gender," she said.
The premier hoped that the thousand-year-old bond of communal harmony of Bangalis would be retained with the united effort of all to create a "Sonar Bangla," as envisaged by the Father of the Nation Bangabandhu Sheikh Mujibur Rahman.