Commander Stuart Cundy said the death toll, which has risen from 58, may still change, but not by as much as it had in recent days.
Photos and videos published by the Metropolitan Police show the gutted wreckage of apartments within the 24-storey tower block after Wednesday's fire.
The deadly blaze in the social housing block has led to growing public anger.
The 1974-built concrete tower had recently been fitted with new exterior insulation cladding, which many locals blame for spreading the inferno so quickly.
One minute's silence held for victims of the London tower fire
Cundy promised an "exhaustive" criminal investigation into the fire that would also look at a major refurbishment of the building completed last year.
"We will go where the evidence may take us," and do everything possible "to ensure that those responsible will be brought to justice," he said.
"If I identify... an issue that is a risk to public safety, we will be sharing that immediately with the relevant authorities," he added.
London tower fire footage released
The government has set up a £5 million emergency fund for the Grenfell Tower residents, allocating a minimum £5,500 to each household with £500 cash payments already being handed out.
Authorities are still searching for victims and Cundy said the intensity of the fire may mean some people will be unable to be identified.
He also said that five people who were reported missing had now been found safe and well.
A minute of silence is being held across the United Kingdom to pay tribute to the victims of the fire.