"When an existing building is undergoing a renovation, upgraded fire safety measures may be required depending on the type of insulation and cladding proposed as part of the renovation", he said.
Two Tube lines have been partly suspended amid safety concerns at Grenfell Tower.
More than 250 firefighters tackled the blaze in north Kensington as London Fire Commissioner Dany Cotton said the scene looked like a "disaster movie".
Flowers and posters of missing persons are still taped to the gates of the church, which has been used as a temporary shelter and gathering point for donations.
The attempt to quell the growing anger over her response to the fire comes as May is under unprecedented pressure following her party's loss of its parliamentary majority last week in the country's general election.
The fire triggered both sorrow and outrage, as residents described the futility of their earlier attempts to have the building's safety issues addressed, particularly its fire escape plan.
David Lammy said Sunday he is anxious that documents will be quietly deleted and disposed of as police begin a search for evidence.
The family's lawyer Maria Cristina Sandrin said: "I've heard the recording of Gloria talking to her mother and there is no hope to find them alive".
Mrs May said: "As we continue to respond to the needs of the community, our focus is on ensuring that all of those affected by this unimaginable tragedy get the right support as quickly as possible". He says trust in the authorities is "falling through the floor". "So that 58 would include that 30", he said.
One member of Parliament has called for corporate manslaughter charges after learning flammable material was used to clad the building during a recent renovation.
"We´ve worked tirelessly to establish how many people we believe were in Grenfell Tower on the night and at this point in time we are unable to say that they are safe or well", he said. He says it will take weeks or longer to recover and identify all the dead at the building.
He said the situation has become an emergency and that "all assets" should be brought to the table.
Late Sunday, the Metropolitan Police released three photos from inside Grenfell Tower, which showed in close detail how the fire charred the 24-story building that once housed up to 600 people in 120 apartments.
Dozens of people attended a meeting of the Radical Housing Network, made up of different activist groups, in a community centre not far from the burnt-out tower block on Saturday morning to discuss their next steps in supporting displaced residents.
With anger mounting over the government's handling of the blaze, May met residents from the Grenfell Tower and pledged to support the victims as protesters gathered to demonstrate in the streets around her residence for a second day.
He also formally identified the first person known to have died as 23-year-old Mohammad al-Hajjali, a Syrian refugee.
The new exterior cladding used in a renovation on London's Grenfell Tower may have been banned under United Kingdom building regulations, two British ministers said Sunday as police continued their criminal investigation into the inferno that killed at least 58 people.
Other victims have been named by their families.