He added: "We would like the chief executive of the council to make public commitments on what the council is going to do for the victims of this borough, and for all the other buildings in the borough that could stand the same fate at Grenfell Towers". Demonstrators gathered outside, protesting about several issues including the fire.
London is reeling from Wednesday's early morning blaze, which charred the bulk of the 120-apartment tower in the city's Kensington neighborhood. British media have reported that contractors installed a cheaper, less flame-resistant type of exterior paneling on the 24-story tower in a renovation that was completed just past year.
Of the 58, 30 people are confirmed dead.
Pressed again on whether she had failed to understand the anger felt by the public, she said: "This was a bad tragedy that took place".
"The scale of this tragedy is clearly proving too much for the local authority to cope with on their own", Mr Khan said in an open letter to Ms May.
Some later left the red-brick building near Kensington High Street, a luxury shopping district, but around 30 remained inside in a tense standoff with about 30 police officers and a dozen security guards.
Commander Stuart Cundy said 58 people who were in Grenfell Tower on the night of the blaze are missing and presumed dead.
Cundy made a plea to anyone who escaped the tower but hasn't checked in with police to come forward. Of the 20 people found by emergency services so far, six were outside the tower, while it has not yet been deemed safe enough to recover the 11 bodies found inside.
After meeting with Grenfell survivors on Friday, Ms May announced a 5 million pound (AUS$8 million) fund to help them and expressed sorrow for their plight. "Hundreds of people get stranded at airports all over the world", he said. "It should define the leadership of May and she should be forced to resign", he said.
But the identification of the victims appears to be proving very hard, which experts attribute to the extreme heat of the fire.
LeT leader, 2 civilians among 14 killed in Kashmir unrest
The victims were travelling in a police jeep on the Anantnag-Achabal road when the incident occurred. The militants started indiscriminate firing at the police party using their assault rifles.
The Metropolitan police have officially begun a criminal investigation into the fire. They paid their respects before the start of the annual Trooping the Color procession that marks the observance of the queen's birthday.
"It is hard to escape a very sombre national mood", she said in a message marking the event.
But public anger has been swelling, with furious residents heckling May and storming the local authority headquarters on Friday.
The government has promised a full public inquiry, but that has done little to a sense of frustration at the lack of information about how the fire moved so quickly to engulf the building.
"All our warnings fell on deaf ears and we predicted that a catastrophe like this was inevitable", the group said after the fire broke out, according to the Associated Press.
May has faced a barrage of criticism for the government's initial response to the tragedy at Grenfell Tower.
Their teams were forced to leave the 24-storey building yesterday afternoon when the fire restarted, delaying further the efforts to reach upper floors - where many victims are thought to have been trapped. Numerous displaced are living in churches and community centres. "I knew them. I watched the flames".
"Our focus has been on those that we know were in Grenfell Tower".
The package includes a guarantee to rehouse people as close as possible to where they previously lived - a poor neighbourhood surrounded by extreme wealth.