He said that number could change should further information come to light. Some 70 residents remain unaccounted for.
On Thursday, May was pictured speaking to emergency workers, but was kept away from the public.
Police also said that the number of people missing and assumed dead had risen from the previously official toll of 58.
Ms Alia Al-Ghabbani, a receptionist who lives in the estate, was among many angered by a recent refurbishment in which new cladding was added to the exterior of the building and which media reports said might have played a part in the rapid spread of the fire.
It will take weeks or longer to recover and identify all the people who died, he said.
Local residents also say they are angry that their safety concerns had been ignored and that people had been told to stay in their flats in the event of a fire.
Speaking on Friday evening, Mrs May said: "Everyone affected by this tragedy needs reassurance that the Government is there for them at this awful time - and that is what I am determined to provide".
More than 20 police officers rushed into the town hall to restore order and mounted police were on stand-by. He asked anyone who was in the tower and survived to contact police immediately.
He said the government is carrying out an "urgent inspection" of other tower blocks in Britain to assess safety.
One woman wept, saying it was because the PM declined to speak to anyone outside the meeting which lasted less than hour.
First Secretary of State Damian Green, May's deputy, said the prime minister was "distraught" and shared "the same degree of sympathy and horror" as everyone else.
The identification of the victims is proving very hard - which experts attribute to the extreme heat of the fire.
Officials are using dental records, fingerprints, DNA samples, tattoos and scars to try and positively identify victims.
"Wallowing in the wash of a general election that stripped our prime minister of her authority on the very eve of European Union negotiations, neither common sense nor the evidence suggest she can re-establish public confidence", Parris wrote in the Times.
Queen Elizabeth II said the disaster had cast a sombre pall over Britain, but insisted the country was showing resolve in the face of adversity.
But she sidestepped questions over whether she had failed to judge the public mood.
The tragedy has provoked a huge response from nearby communities. More than 3 million pounds ($3.8 million) have been raised for the victims.
"It was a death trap, and they knew it", one person shouted as demonstrators surged inside the offices of the Kensington and Chelsea council, responsible for managing the social housing block in a working-class enclave of one of Britain's richest districts.
Appearing on the BBC's Andrew Marr Show, Mr Hammond said: "My understanding is the cladding in question, this flammable cladding which is banned in Europe and the U.S., is also banned here".