"In keeping with tradition, PM Narendra Modi presents a memento to President on the occasion of farewell hosted by him for the President," a Press Information Bureau tweet said.
The dinner was attended by President-elect Ram Nath Kovind, Bihar Chief Minister Nitish Kumar, senior ministers and various opposition leaders.
Mr Mukherjee will be given a farewell by MPs on Sunday in the Central Hall of Parliament.
In a simple function held at the Manekshaw Centre, the President interacted with senior military officers and in his farewell address, extended his best wishes to all members of the armed forces and their families. He also paid tributes to the martyrs and their families for their sacrifices for the nation.