It includes 30 deaths that already have been confirmed, and reports of people who are missing and presumed to have been killed.
He said five of the dead had been formally identified, and it would be a slow and painstaking task to identify the others because of the intensity of the fire.
The fire ripped through the high-rise early Wednesday.
Council leader Nicholas Paget-Brown says questions about how the fatal fire spread so quickly through the tower block "will be answered".
His call was echoed by London Mayor Sadiq Khan who wrote an open letter to Theresa May demanding that she confirm "as a matter of urgency" that everyone from Grenfell Tower and other evacuated properties "will be rehoused locally immediately".
He said he was not interested in knowing why they had left it so long to make themselves known, but stressed that it was vital for police to know they are safe and well.
Police had warned the death toll might rise as search operations continued in the charred shell of the building.
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A Department of State spokeswoman said that out of respect for the privacy of Warmbier's family, "we have no further comment". After a short trial on 16 March , Mr Warmbier was given a 15-year prison sentence for crimes against the state.
His remarks came as Nick Paget-Brown, the Tory leader of Kensington and Chelsea council, insisted officials were on the ground "very soon" after the fire broke out following criticism from Prime Minister Theresa May, who said the support given to residents was "not good enough".
The meeting lasted more than two hours Saturday but the group did not speak to reporters gathered outside.
She has promised to set up a public inquiry and pledged 5 million pounds of support, housing guarantees and help with access to bank accounts and cash.
May said after the meeting Saturday that there have been "huge frustrations" in the community as people tried to get information.
"I have heard the concerns and I have ordered immediate action across the board to help victims' relatives and the survivors", May said.
The 23-year-old Alhajali is the only victim of the Grenfell Tower fire to be officially named as the hard process of identifying human remains continues.
Some 19 patients are still being treated in hospital, of whom 10 are in a critical condition, the National Health Service said.
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The outcome of leaving the EU, its single market and customs union without a future trade deal lined up. It has also spoken out on what Britain's financial settlement with the European Union ought to entail.
Toronto Fire officials spoke out after the Grenfell Tower inferno to assure residents that protections in the Ontario Building Code and routine fire safety inspections will prevent a similar incident here. This relies on dental records, fingerprints and DNA when possible and also features like tattoos or scars.
The queen and her husband, Prince Philip, stood silently on the steps of Buckingham Palace before the start of the Trooping the Color that each year marks the queen's official birthday, which is traditionally celebrated in June when the weather is warm.
"Put to the test, the United Kingdom has been resolute in the face of adversity", she wrote".
But public anger has been swelling, with furious residents heckling May and storming the local authority headquarters on Friday.
May later announced that the public inquiry looking into the tragedy will report directly to her, the AP said.
Cundy had earlier expressed fear that all the victims of the massive fire that engulfed the Grenfell Tower in west London may never be identified as there was growing anger over the failure of authorities to ensure the fire safety of the residential block.
The extensive use of fire-resistant glass panels on the building's exterior could prevent fire from spreading upward quickly.
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Both officials are listed as members of the American Technology Council . CEO Jeff Bezos; Oracle Co-CEO Safra Catz; Alphabet Inc. The meeting was also notable for who didn't attend.
The tragedy has provoked a big response from nearby communities that have donated food and shelter to the victims.