He says it may be necessary for numerous outmoded tower blocks built in the 1970s to be demolished because of safety concerns.
Protesters stand in the lobby of Kensington town hall in west London, the headquarters of the Royal Borough of Kensington and Chelsea, demanding answers over the Grenfell Tower fire, in London, Friday June 16, 2017.
Authorities believe 58 people have died in the Grenfell Tower inferno. With Brexit talks starting Monday, the premier is still trying to broker a deal with Northern Ireland's Democratic Unionist Party that will allow her to get legislation through Parliament.
On the other hand, Labour Party leader Jeremy Corbyn, whose party recently ran a promising campaign against May's Conservatives leading to her party losing the majority, was seen visiting and hugging tearful relatives of victims near the burnt building after the fire, the report said.
Demonstrators from the Grenfell Tower area had gathered to protest the council's failure to act on warnings over fire safety in the building.
Metropolitan Police commander Stuart Cundy has said that there are still some bodies in Grenfell tower but conditions have been too hazardous to retrieve them.
"(This aims) to give the victims the immediate support they need to care for themselves and for loved ones", May said.
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.
Some residents had warned months ago that the tower represented a risky fire risk.More news: Shale oil boom to hurt OPEC well into 2018
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Kate Taylor, who lives about 3 miles from the tower, said she joined the protest to show solidarity with the victims, and said she agreed with the shouts of "Tories out".
Among the questions being asked are whether the owner of the building took any shortcuts in its use of construction materials, including the installation of external cladding, part of a renovation completed a year ago, that may have accelerated the fire's spread: It took only 15 minutes to take hold across the tower block.
Did cheap cladding panels fuel the fire?It has since emerged that the United States had banned the type of cladding thought to have been used on Grenfell Tower.
Local residents also say they are angry that their safety concerns had been ignored and that people had been told to stay in their flats in the event of a fire.
Hours before the fund was announced, London's Mayor Sadiq Khan wrote an open letter to May over the perceived lack of government response.
Police said on Saturday that their investigation would look at the building and its 2016 refurbishment, and vowed to bring prosecutions "if there is evidence".
One was Gloria Trevisan, 26, an Italian architect living in London because her family was having financial difficulties at home in Italy. A blaze at a building in Melbourne, Australia, in 2014 was later directly linked to the type of combustible cladding in place on the structure and triggered an audit of numerous city's high-rises.
Queen Elizabeth II and her grandson Prince William visited a community centre Friday where some of the survivors are being housed, and where volunteers have been inundated with donations of clothes and food.
The identification of the victims is proving very hard - which experts attribute to the extreme heat of the fire. When protesters heard the news, they responded: "It's not enough, we've basically raised that much online already".