He said the government is carrying out an "urgent inspection" of other tower blocks in Britain to assess safety.
Days after a blaze tore through Grenfell Tower in London, the death toll continues to rise: City police announced Saturday that 58 people "are missing and we assumed likely to have died".
So far 30 people are confirmed dead but police said this weekend that based on reports from the public the number now stood at 58 and that this could rise.
The tragedy has only added to pressure on May to step down, after her decision to hold a snap election earlier this month ahead of Brexit talks backfired, weakening her party and leaving it unable to govern alone.
More than 250 firefighters tackled the fire at the 24-storey tower block in north Kensington on Wednesday, June 14.
The Prime Minister insisted the Government was doing everything possible to help those caught up in the tragedy.
May herself had come in for a barrage of criticism for failing to visit residents and her response to the disaster.
Victims met the Prime Minister at Number 10 on Saturday evening and man representing the group said they had spoken about their "demands and what we expect".
Suspect held in mosque attack in London
He was arrested on suspicion of the commission, preparation or instigation of terrorism including murder and attempted murder. A vehicle struck pedestrians near a mosque in north London early Monday morning, causing several casualties, police said.
"Those who mock health and safety, regulations and red tape need to take a hard look at the consequences of cutting these and ask themselves whether Grenfell Tower is a price worth paying". "This is an absolutely terrible fire that took place", May said.
Fire safety experts believe that cladding put on the building's exterior during a renovation previous year was less fire retardant, which may have fueled the blaze.
London police late Sunday released photographs of the devastation inside the 120-unit building to show the public and frustrated family members why the search for victims is taking so long. Community groups have said that warnings about poor fire safety have always been ignored, and that in the aftermath of the disaster, officials failed to immediately take care of those affected.
The Prime Minister will chair another meeting of the Grenfell Tower Recovery Taskforce at 11am tomorrow.
The first victim to be formally identified was Mohammed Alhajali, a 23-year-old Syrian refugee, who came to Britain in 2014 with his brother.
However, May retracted the pledge on Saturday night, said that the residents would be found homes in the same borough or neighboring ones. Clement's Church near Grenfell Tower.
In an interview with the BBC, Mrs May promised a public inquiry into the disaster and pledged that survivors would be rehoused within weeks.
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