It said: "We are devastated by this tragedy".
But on Friday she continued to sidestep questions over whether she had failed to grasp the mood of the public by failing to meet with residents in the fire's immediate aftermath.
On Saturday more than 1,000 people gathered near May's Downing Street office to protest against her plan to form a government with the support of a socially conservative Northern Irish party.
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 Mrs May, who said the support given to residents was "not good enough". "The police are saying they couldn't tell us anything until they have more information", he said. He says it will take weeks or longer to recover and identify all the dead at the building.
"The fact is they looked at profit above safety and that says it all". Firefighters were using drones and sniffer dogs to search the blackened tower, as some of the upper floors have not yet been made safe.
"My heart goes out to those affected", Cundy said.
Mr Hammond said a criminal investigation would examine whether building regulations had been breached when the block was overhauled.
They say their complaints were ignored - and fear it was because the tower housed mainly poor people in a hugely wealthy neighbourhood. A new sign was put up, removing that detail.
"This was a bad tragedy that took place", she said Friday.
The latest figure included the 30 already confirmed to have died in the devastating fire on Wednesday.
Two Underground lines near the fire area were partially shut down on Saturday to make sure that debris did not land on the tracks.
Major roads near the stricken building were open Saturday.
The announcement by a spokesman comes a day after May was heckled during a visit to the west London neighborhood where Wednesday's inferno took place.
"I have stressed to the task-force the need for local residents and the wider public to be provided with as much information as possible and for there to be maximum transparency".
The UK government has promised that all those left homeless by the disaster will be rehoused in the local area.
The monarch stood for a minute's silence before her 91st birthday parade on Saturday.
"It is hard to escape a very somber national mood", Elizabeth said in a message.
Twenty-four injured survivors are still being treated, 12 of them in critical care.
"I've heard stories of heroism, from Christians, from Muslims and from others, looking after their brothers and sisters, their neighbours and doing the job that we expect from this brilliant community because of the fantastic community that is here in this part of London".
The comments came as former chief fire officer Ronnie King told the Observer newspaper that urgent requests for meetings with ministers and action to tighten rules were stonewalled.
One member of Parliament has called for corporate manslaughter charges after learning flammable material was used to clad the building during a recent renovation.
"People lost everything in the fire and were left in only the clothes they were wearing".
Londoners and others have also donated huge amounts of food, water and clothing, and shelter, to survivors.