This is Mrs May's second meeting with those affected by Wednesday morning's fire, which was described as "unprecedented" by London's Fire Brigade Commissioner. Suspicions have grown that flammable materials were used to clad the building and accelerated the spread of the fire.
A woman touches a poster for 12-year-old Jessica Urbano on a tribute wall Friday after laying flowers on the side of a church next to the Grenfell Tower in London.
Public anger is mounting as residents and neighbors demand answers for how the blaze early Wednesday spread so quickly and trapped so numerous tower's 600-odd residents.
He promised an "exhaustive" criminal investigation that would also look at a major refurbishment of the tower completed a year ago.
Of the total 58 people missing, presumed dead by police, there are at least 30 confirmed deaths.
London firefighters are continuing the grim search after a high-rise fire that killed at least 30 people as public anger about the blaze continues to grow.
He says it may be necessary for numerous outmoded tower blocks built in the 1970s to be demolished because of safety concerns.
Police say 24 injured people remain at the hospital.
On the figure of 58, he said: "I really hope it won't, but it may increase", while adding that "it might be that some of those are safe and well", and for some reason, had not yet made themselves known to the police.More news: Taliban Storm Afghan Police Compound, Kill Five Police
More news: Irish, British PMs to meet to talk Brexit, N.Ireland crisis
More news: Uber considering the future of CEO Travis Kalanick
As part of the inquiry, prominent Labour politician David Lammy said the government and police must seize all documents and records related to the building's renovation to avoid the destruction of incriminating evidence.
Tower residents and many others in the area are still struggling to come to terms with what they have seen and lived through.
He says tower residents who survived fear a cover-up will keep the truth from coming out.
May announced £5 million, or $6.4 million, in aid to help victims of the Grenfell Tower fire pay for emergency supplies like food, clothing and other items.
He said the community in north Kensington, west London, was "frustrated and, yes, angry".
British Prime Minister Theresa May, facing criticism for the government's handling of the disaster, met Saturday with a small group of fire survivors invited to her official residence at 10 Downing Street.
The identification of the victims is proving very hard - which experts attribute to the extreme heat of the fire.
Britain's government says it will act on recommendations from a probe into the London tower block fire, responding to a disaster critics said showed something had gone "badly wrong" in the country.
The Government has also announced that a minute's silence will be held for the victims at 11am tomorrow.
She said earlier that the national mood is somber but that Britain is resolute in the face of adversity.