The artist also criticised the representation of the Americas in the British Museum.
But Fischer has rejected calls to reduce the museum's European collection and insisted work is already underway to modernise exhibits with a strong presence from all areas of the world.
Fischer said: 'Sir Antony Gormley is right to say that the British Museum should be modernised and the display of the connection renewed.
'This is precisely the plan that we have been developing since my appointment as director in 2016, and is one of the many reasons I do not accept his view that some of the museum's objects should be removed from the collection.