Trade Minister Greg Hands said the government is carrying out an "urgent inspection" of the roughly 2,500 similar tower blocks across Britain to assess their safety, while an opposition lawmaker urged the government to quickly secure documents in the Grenfell renovation for the criminal probe.
Cundy says the new number may change as investigation continues.
The latest figures from NHS England show that 17 patients are still being treated in four London hospitals.
London Fire Commissioner Dany Cotton told BBC Radio 4's Today programme she could understand the "absolute frustration and misery" of people concerned about loved ones who had not yet been identified, but that it was critical to go through the process properly.
He said it had been "incredibly emotional working in there", adding: "On Saturday I went in myself and went to the top floor".
Conservative Prime Minister Theresa May has announced a fund of £5 million ($6.4 million) to help those affected by the blaze.
"As we do everything we can to help them, we will make sure they have the counselling and emotional support they need in the hard days, weeks and years ahead".
They were reported missing by Catherine Lindsay - who was teaching them English - but the family has now been found.
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Hundreds have been left homeless by the blaze, putting more pressure on officials in a city already plagued by a chronic housing shortage.
Mr Green said the probe will look at whether sprinklers should be retrofitted to tower blocks and the Government will "follow the recommendations of the public inquiry".
This will ensure those involved in the response to the tragedy are able "to receive targeted support should they need it", Downing Street said. "We do not want another fatality arising out of this tragedy". More than 3 million pounds ($3.8 million) have been raised for the victims. Many questions also center on the speed at which the fire spread.
She also chaired the government's Civil Contingencies Committee, which deals with major crises such as terrorism or natural disasters, in Whitehall.
"There is considerable damage within Grenfell Tower", he said.
Asked about this by the BBC's Andrew Marr, The Chancellor said: "My understanding is the cladding in question, this flammable cladding which is banned in Europe and the United States, is also banned here".