Grenfell Tower fire: Seventy-nine people feared dead
Met Police Commander Stuart Cundy confirmed the figure in a statement on Monday, adding it may still change.
Fire swept through the 24-storey block in North Kensington, west London, shortly before 01:00 BST on 13 June.
Many of the families that were affected lost more than one relative, said Mr Cundy, adding that his "heart went out to them".
Of those who were injured, 18 people remain in hospital, with nine in critical care.
Mr Cundy said his priority was to identify the people who died in the building and to remove them as quickly as possible.
But he warned that not everyone would be identifiable and the operation would take "many, many weeks".
London fire fighters observe minute silence
A minute's silence was held at 11:00 BST across the UK to remember the victims.
Earlier, police also released new images from inside the 24-storey building to show the scale of the challenge they face.
The government has sent in a team of civil servants to to help with the relief effort.