In a condolence message to his son Ashok Bardhan, the president said the nation had lost an "outstanding public figure and a dedicated trade union leader".
"I am deeply saddened to know about the demise of your father AB Bardhan... he was a personal friend and colleague of long years."
"Widely respected for his wisdom and commitment to the poor, Bardhan's influence extended across the political spectrum. As a veteran leader of the CPI, he made immense contribution towards advancing the cause of the working class."
In his passing away, the nation has lost a dedicated trade union leader who was always in touch with the grassroots of society, he added.
The Communist Party of India (CPI) leader died at a hospital here on Saturday. He was 92.