Writing in the Observer, Mr Khan said it may well be the "defining outcome of this tragedy that the worst mistakes" of that era become a thing of the past. "This is an incredibly distressing time for all of them".
Five people who had been missing following the fire at Grenfell Tower have been found "safe and well".
Metropolitan Police Commander Stuart Cundy announced the new number - up from 58 - in a statement to reporters.
"Equally, there may be people who thankfully may have managed to escape the fire and for whatever reason have not let their family or friends or police know", he said.
Shortly after the fire broke out at 1am on Wednesday June 14, courageous little Ariel went into his mum's room and said "Mum, I think there's a fire".More news: Technology CEOs urged to join Trump initiative
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The fire ripped through the high-rise early Wednesday.
Although police did not speculate on the eventual number of fatalities, local community sources say at least 70 from Grenfell Tower are still missing, including entire families. He expects the operation to last "many, many weeks".
On Friday, William and Queen Elizabeth II visited the victims of the Grenfell Tower fire that killed as many as 58 people last week. The death toll is expected to rise, as at least 60 people remain unaccounted for.
Members of the emergency services join people in a minute's silence for the victims of the Grenfell Tower fire near the site of the blaze in North Kensington, London, on Monday. "We have to address these issues".
Records have shown that in a renovation a few years ago, the building was re-clad with siding that may have had "a polyethylene core", rather than a more fire-resistant mineral core, as NPR's Frank Langfitt reported.
"As recent bad events in London and Manchester have brought to light, Blue Light workers do an extremely challenging job, encountering hard and traumatic situations", he said.
As the investigation began, Cundy urged missing residents who are alive and have not come forward to contact authorities to ensure their safety. "It will also be a subject that the criminal investigation will be looking at", he said.