Speaking after visiting the site of the devastating fire in North Kensington, London, May said she wanted to make sure "this terrible tragedy is properly investigated."
London's fire chief said there was little chance of finding anyone else alive in the charred remains of the tower. Dozens of people remain missing.
May's government was facing growing questions about why ministers did not act on recommendations following an earlier fire in London, which led to calls for sprinkler systems to be installed in residential blocks and for a full review of Britain's fire regulations.
A prominent London Member of Parliament, David Lammy, of the opposition Labour Party, said corporate manslaughter charges should be brought against those held responsible for the tragedy.
Firefighters were still working to dampen the blaze and search for remains of the dead Thursday. D
Dany Cotton, London's fire commissioner, said she had "genuinely" no idea about how many people were still missing. She admitted that it we be an "absolute miracle" if there was still anyone alive in the tower and that it would take "weeks" to complete a proper search with the building still unstable.
Cotton said that urban search and rescue dogs would be deployed inside the building. While the core of the building was structurally sound, dogs were lighter and more agile than people, she said. Her staff will remain on scene for "days to come" and that the search of the tower would be a "slow and painstaking process."
Cotton also said that parts of the building would have to be shored up in order to make it safe for rescue workers to reach each floor.
May praised the actions of the emergency services and the local community in coming together at such a difficult time.
She also sought to reassure residents who had lost their homes that they would be rehoused in London and as close as possible to the local area.
"We need to know what happened, we need to know an explanation," she said. "We owe that to the families, to the people who have lost loved ones and the homes in which they lived."
The London mayor, Sadiq Khan, said in an earlier call for a public inquiry that it should produce an interim report by the summer.
Anger
Lammy, the London Labour MP, called for arrests to be made over the fire, describing the incident as "corporate manslaughter." Lammy told the BBC he had yet to hear from family friend Khadjia Saye who lived in the tower, and called the fire "an outrage".
"We built buildings in the 70s, those 70s buildings, many of them should be demolished, they haven't got easy fire escapes, they've got no sprinklers - it's totally, totally unacceptable in Britain that this is allowed to happen and people lose their lives in this way and people should be held to account."
Questions remain over how the Grenfell Tower fire began and how it spread so quickly through the 1970s-era building that was home to as many as 500 people.
Originally constructed in 1974, the residential tower block had recently undergone a massive $13.2M (£10.3M) refurbishment carried out by private developers Rydon and completed in the summer of 2016. Questions were focused on exterior cladding that was added as part of the refurbishment.
British Prime Minister Theresa May speaks to Dany Cotton, Commissioner of the London Fire Brigade at the scene.
Many of those evacuated said the fire had spread incredibly quickly with almost no warning and multiple residents told CNN they did not hear fire alarms when the blaze broke out.
Residents had complained about safety going back several years.
In November a residents group, the Grenfell Action Group (GAC), highlighted ongoing concerns among residents over the safety of the tower, managed by the Kensington and Chelsea Tenant Management Organisation (KCTMO) on behalf of the borough.
The blog post argued that only "a catastrophic event will expose the ineptitude and incompetence of our landlord ... and bring an end to the dangerous living conditions and neglect of health and safety legislation that they inflict upon their tenants and leaseholders."
KCTMO acknowledged residents' concerns in a statement. "It is too early to speculate what caused the fire and contributed to its spread. We will cooperate fully with all the relevant authorities in order to ascertain the cause of this tragedy."
"We are aware that concerns have been raised historically by residents. We always take all concerns seriously and these will form part of our forthcoming investigations."
Safety concerns
Many questions are still unanswered, chief among them, how the fire spread so quickly.
Ian Burgess, a professor of structural engineering at the University of Sheffield, told CNN that while fires do spread vertically up buildings, it's "generally quite a slow process."
"This was clearly a very rapid transmission of flame up the front of the building," he said.
Shock over how quickly flames engulfed building
Shock over how quickly flames engulfed building 02:42
Mike Gilmartin, director of Omega Fire Engineering, said that to meet requirements, a building must have residential sprinklers and fire alarms in every apartment, as well as other features such as a firefighting shaft.
Gilmartin said fire design has evolved over the years but it's not feasible to make all older buildings comply with the latest legislation. He added it's standard guidance that residents should stay in their apartments if a fire breaks out, as many of those in Grenfell Tower did.
"It is considered that occupants are safer in their dwelling than coming out into potentially smoke logged corridors," he said.
A 2009 fire at a residential block in south London, Lakanal House, led to calls for sprinkler systems to be installed in similar buildings. The government repeatedly committed itself to reviewing fire standards in buildings, but to date has not yet done so.
