Mr Mukherjee, Dr Singh and Congress vice president Rahul Gandhi were the first ones to pay floral tributes to the late prime minister at 'Shakti Sthal' where she was cremated, while PM Modi took to Twitter to pay his regards.
"Tributes to former PM Mrs Indira Gandhi on her death anniversary," PM Modi said in a tweet.
Later, Dr Singh and Rahul Gandhi also attended a prayer meeting at the Indira Gandhi Memorial at 1 Akbar Road in Delhi.
Many former union ministers, senior Congress leaders and MPs were also present at both the places.
Rahul Gandhi put out a tweet remembering the words of his grandmother along with her picture saying, "Forgiveness is a virtue of the brave: Indira Gandhi."
Congress President Sonia Gandhi could not attend the programmes as she has just returned home after being admitted to a hospital.
Indira Gandhi, the then prime minister, was assassinated on this day in 1984 by two of her security guards.