While the blaze has prompted an outpouring of generosity, with many people donating provisions and clothes, it has also unleashed rage at the authorities as the charred tower was cast as a deadly symbol of a deeply divided society.
Dozens of demonstrators surged towards the entrance and there were scuffles outside as organisers appealed for calm.
May, whose political position was already weakened by a poor showing in parliamentary elections last week, announced the government would immediately provide 5 million pounds ($6.39 million, 5.7 million euros) to help victims of the fire.
Queen Elizabeth II visited West London to meet with those who were affected by the fire, as did Labour Party leader Jeremy Corbyn. Officials cited security concerns and suggested she didn't want to distract police and others from their work.
The group of residents, who were wearing white wristbands as a show of solidarity, left and briefly told cameras they would be making a full statement "in the community" following the meeting.
Opponents said May's handling of the fire had thrust her position further into doubt by showing a failure to feel the public mood and act decisively.
They said he was a "very awesome and kind person" who "came to the United Kingdom because he had ambitions and aims for his life and for his family".
The Queen and Duke of Cambridge went to temporary relief centres on Friday where they met volunteers and residents who had lost everything.
Eoghan Murphy's call came in response to the fire at London's Grenfell Tower earlier this week in which 30 people have been confirmed dead (the death toll is expected to rise significantly).
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The president tweeted Friday, "Despite the phony Witch Hunt going on in America, the economic & jobs numbers are great". The official demanded anonymity because the official was not authorized to be named discussing the deliberations.
"We were seeking a change to the building regulations for that very objective".
Mr Cundy has warned the search and recovery operation is going to take a "significant" amount of time - with both the police and the London Fire Brigade saying it will take weeks to complete.
Families will be provided a named NHS mental health practitioner if they are in need of extra psychological support or if a family liaison officer believes that they are, and obtains their agreement.
Police said the death toll could change.
Twenty-four people are being treated in hospital, including 12 who are in critical care, he added.
Fire crews were again using water to damp down the high-rise building as they began a third day of picking through the debris.
"It says: "[The inquiry] must be empowered to consider all the steps that were, or were not, taken leading up to and contributing to this most bad incident.
RBKC said 110 households had been given temporary accommodation by Friday morning, and added that it was working to find more permanent homes. "If more funding is required, it will be provided", May said, while more than 1,000 protesters rallied outside her residence Saturday.
Ireland's new housing minister demanded that local authorities conduct fire safety checks on every tower block in Ireland "as a matter of urgency", the Times reported.
Amongst the dead was artist Khadija Saye, whose photography is now being exhibited at the Vienna Biennale.