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. He says "my heart goes out to those affected".
Police had previously put the death toll at 30.
She will meet victims, volunteers and community leaders afterwards.
But unlike opposition leader Jeremy Corbyn and London Mayor Sadiq Khan, May did not meet with residents, prompting criticism from locals, media and within her Conservative party. The public is also demanding answers about how the blaze spread so quickly amid reports that the recently-renovated building's exterior paneling fueled the flames.
But she sidestepped questions over whether she had failed to judge the public mood.
The aluminium cladding, called Reynobond, was made by United States company Arconic and had a polyethylene core, which the reports said was slightly cheaper than fire-resistant models by the same manufacturer.
"We need to know what happened", May said in a televised statement.
Mrs May had earlier sidestepped questions over her response to the disaster, after facing criticism of her reaction to the tragedy. Downing Street then subsequently announced £5 million would be spent on clothing, aid and food for those who have been left homeless.
The government has promised a full public inquiry.
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The meeting is unlikely to quell complaints that May has been slow to reach out to fire survivors, despite her announcement of a $6.4 million emergency fund to help the displaced families.
Whole families are said to be among the missing, including Bassem Choukeir, his wife Nadia, her mother Sariyya and the couple's three daughters Mirna, Fatmeh and Zaynab.
"She is as distraught as anyone, as all of us are, we all feel the sadness, we all recognise the anger and can see why people are that angry and the prime minister feels that as much as anyone", he added.
Activists held up posters with pictures of people still missing after the deadly inferno.
Later, demonstrators stormed the offices of Kensington and Chelsea Council over its handling of the crisis amid concerns that earlier renovation work was linked to the dramatic spread of the blaze.
A total of 24 people remain in hospital, with 12 in critical care. These were hard conversations with a tight-knit community that is understandably distraught, frustrated and increasingly angry.
"The country has witnessed a succession of awful tragedies".
Such a direct message from the monarch is rare and indicated the extent of the turmoil in Britain. "He didn't come with a bunch of police.no one even saw her". Her government is also due to launch hard Brexit talks with the European Union on Monday.
"Wallowing in the wash of a general election that stripped our prime minister of her authority on the very eve of European Union negotiations, neither common sense nor the evidence suggest she can re-establish public confidence", Parris wrote in the Times. That is what a prime minister should do and that is what she has done.