Earlier the police figured the death toll at 30. Many chased after her armored cars, prompting the police to intervene and push people back.
Prime Minister Theresa May's government earlier sought to quell anger over the fire, pledging to support the victims of the blaze after protesters jeered her when she visited local residents.
Opposition Labour leader Jeremy Corbyn, London mayor Sadiq Khan, Prince William and Queen Elizabeth, 91, have all visited residents from the 24-storey Grenfell Tower destroyed on Wednesday as many slept, and anger is growing in the community.
Following the meeting, Mrs May released a strongly-worded statement in which she said on-the-ground support for families in the immediate aftermath of the blaze "was not good enough".
Told there was a need for the public to hear her say something had gone badly wrong and the government accepted responsibility, Mrs May said: "Something bad has happened".
"We have identified those buildings and now and over the weekend people are going in and inspecting those buildings".
"I really do understand the frustration of so many about not knowing the scale of the tragedy that's unfolding behind us".More news: Russian opposition leader arrested as protests rage
More news: Syrian army declares 2-day combat cessation in southern city
More news: Rizzo, Cubs rally for 6 runs in 9th to beat Pirates
The cause of the fire is not yet known. When May finally went out to meet with victims at St.
She said she has ordered daily progress reports on housing for those affected, and vowed the public inquiry into the disaster will be "open and transparent". Those who lost their homes will be rehoused within three weeks, she said.
My commitment to families is that as soon as we can, we will locate and recover their loved ones.
"The Prime Minister is distraught about what has happened", said Green, who was appointed May's deputy in the wake of the general election.
"I would like to ask anyone who was in Grenfell Tower that night, but for whatever reason has not told us they are safe to please call our Casualty Bureau", he said.
The fire has also become a symbol of class inequality - the Grenfell Tower's charred remains stand high above one of the British capital's wealthiest neighborhoods.
She said it was "difficult to escape a very sombre mood".
Defending the way Mrs May had handled the tragedy, First Secretary of State, Damian Green said suggestions the Prime Minister does not seem to have what it takes to respond to such a disaster were "terribly unfair".
"This should not be happening in the United Kingdom, this should never happen".