The Prime Minister said there had been "huge frustrations" on the ground as people struggled to find information.
"The response of the emergency services, NHS [National Health Service] and the community has been heroic", May said in a statement released Saturday after the prime minister met with victims and community leaders.
Asked if there were angry exchanges, he said: "We tried to hold it well as a meeting".
Confirming the latest death toll, Metropolitan Police commander Stuart Cundy said the tower remained "in a very hazardous state" but there was "nothing to suggest at this time that the fire was started deliberately". "I really hope it won't, but it may increase". "United in our sadness, we are equally determined, without fear or favour, to support all those rebuilding lives so horribly affected by injury and loss", she added. "We need to know exactly the number of people who were there during this tragedy".
"Both myself and colleagues from London Fire Brigade have already said it will take weeks".
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Families and friends make desperate appeals for people trapped in building.
Cundy said police will investigate the tower's refurbishment project, which experts believe may have left the building more vulnerable to a catastrophic blaze.
On Saturday, she invited a group of residents and community leaders to Number 10 Downing Street for a two and a half hour meeting to listen to their concerns.
"Sadly, it is expected that the total will rise and it is not expected that any survivors will be found", he said. But she said the welfare of her loved ones was more important.
Specialist sniffer dogs are on the scene to identify victims in the ashes.
After her visit, Mrs May said: "Everyone affected by this tragedy needs reassurance that the Government is there for them at this bad time - and that is what I am determined to provide".
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Rescue personnel have had difficulty reaching the top floors of the charred, 24-story tower.
Some Grenfell residents had warned months ago that fire safety issues at the tower left it at risk of a "catastrophic" event.
"We're all desperately sad, we're all angry, but of course none of us as angry as those who were directly affected". Numerous displaced are living in churches and community centers.
Cundy promised an exhausting investigation into the tragedy. "They feel the Government and local council haven't done enough to help them in the aftermath of this horrific incident, or to provide answers to their increasingly urgent questions".
"Our criminal investigation will identify any criminal offences that have been committed".
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