Emergency services are continuing to search for bodies in the now burnt-out building.
"The package of support I'm announcing today is to give the victims the immediate support they need to care for themselves and for loved ones".
Meanwhile, dozens of people erupted into Kensington and Chelsea town hall to protest the lack of response following the fire.
The London Evening Standard reported that hundreds of activists marched to the town hall and gathered outside the building on Friday chanting: "We want justice".
When asked why they couldn't get access to it, she said: "Because no one's telling us where it is".
If that death toll is confirmed, it would make the Grenfell Tower blaze the deadliest in London since the Second World War. Like many other residents she has spent the days following the fire living in temporary shelters with minimal sleep, printing and distributing posters wherever she can.
In an interview, she was questioned over whether there was a need for the United Kingdom government to accept some responsibility for what had happened.
Other measures outlined by Prime Minister Theresa May following a meeting with residents at Downing Street on Saturday, included more staff covering phone lines and ground staff wearing high-visibility clothing so they could be easily found.
It tore through all floors of the building and took more than 200 firefighters and 24 hours to bring it under control.
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Mrs May said the public inquiry into the fire will take place "as soon as possible" and insisted the Government had acted on previous warnings about tower block safety by a coroner. "How did they allow this tragedy to happen when it could have easily been avoided?"
Questions are growing about how the flames spread so quickly, engulfing the tower's 120 apartments in what fire chiefs said was an unprecedented blaze.
The move came after strong criticism from London's mayor, Sadiq Khan.
Commander Stuart Cundy said "my heart goes out to those affected".
In a statement, Mrs May said: "The individual stories I heard this morning at Chelsea and Westminster Hospital were horrific".
London police said an investigation, led by a detective from its homicide and major crime unit, would examine whether criminal offences had been committed although they said there was nothing to suggest the fire was started deliberately.
Cundy said there was "a risk that sadly we may not be able to identify everybody".
"Mohammed undertook a risky journey to flee war and death in Syria, only to meet it here in the United Kingdom, in his own home", the Syrian Solidarity Campaign said in a statement.
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