If at least 58 deaths are confirmed, the blaze would be London's deadliest since World War II.
He said: "I thought the way they expressed themselves with a mixture of passion and reason was fantastic, and I hope it's the beginning of a process, not the end of a process, the beginning of a process of real listening between Government, RBKC (the Royal Borough of Kensington and Chelsea council), local residents, that will bring about lasting change".
On Saturday, May met for two hours with 15 survivors and community leaders at her official residence at 10 Downing Street in London.
May was rushed away from a meeting with residents on Friday under heavy police guard as protesters shouted "Shame on you" and hundreds stormed a local town hall calling for justice.
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Her political future - already in doubt after her Conservative Party lost its governing majority in early elections - has been further questioned because of her response to the fire, and observers have even referred to it as her Hurricane Katrina moment.
Mrs May has pledged a £5 million support package for the victims, which included a promise to rehouse them within three weeks.
"Grenfell is where they shove all the people who don't have any choice", said a resident as he watched his home burn.
Scuffles broke out near the Kensington and Chelsea town hall offices on Friday as demonstrators chanting "We want justice!" surged toward the doors. There is ample food and water, but very little privacy or proper bedding, and with the tower destroyed, no one knows where they will be relocated or for how long. I spoke with people who ran from the fire in only the clothes they were wearing.
"I thought they took him outside with me". Unfortunately, that number is only expected to rise as officials continue to search for dozens of missing persons.
He added: "I have said it before, you have my absolute assurance that as soon as I can possibly tell you something that I know to be accurate, I will tell you". "But we need to make sure that that actually happens".
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"As recent awful events in London and Manchester have brought to light, Blue Light workers do an extremely challenging job, encountering hard and traumatic situations", he said.
"It is hard to escape a very sombre national mood", Elizabeth said in a message on her official birthday. "This was a bad tragedy that took place".
Similarly, the mother of Hesham Rahman who also lived in the Grenfell Tower said that her son remains missing.
The prime minister's response, characterized as stilted and lacking empathy, and her failure to meet with fire victims during an initial visit to the site amplified complaints on her leadership.
One woman wept saying it was because the Prime Minister declined to speak to anyone outside the meeting which lasted less than hour.
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