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.
On Friday evening, May was interviewed by Emily Maitlis on the BBC programme "Newsnight" where she sidestepped questions over whether she misread the public mood and anger over the Grenfell fire as well as what her personal response is - leading to more criticism of being called "robotic" and "cold".
In an unannounced tour of the area, the royals went to the Westway Sports Centre close to the tower.
Officials said Friday they are doing everything they can to relocate those displaced by the tower.
He said a police investigation by specialist detectives would "establish the facts to provide, as best we possible, answers for those so deeply and tragically affected by the awful fire at Grenfell Tower". "The Duke and Duchess of Cambridge and Prince Harry are pleased the Evening Standard's Dispossessed Fund has immediately swung into action". They brought us outside.
British Prime Minister Theresa May paid a visit Friday to a refuge center at St. Clements Church, where survivors and the loved ones of victims from this week's fire at Grenfell Tower have congregated.
But that figure could change, he said.
Although police did not speculate on the eventual number of fatalities, local community sources say at least 70 from Grenfell Tower are still missing, including entire families.
Police Commander Stuart Cundy said the number of 58, which was based on reports from the public, may rise and includes the 30 deaths that have already been confirmed.
A top former Conservative politician and Times of London columnist blasted May over her handling of the fire, and said that she must resign.
There was also an outpouring of generosity from the public with many people donating money, provisions and clothes.
On Saturday, NHS England said 19 people were being treated in hospital, including 10 in critical care.
May said after the meeting Saturday that there have been "huge frustrations" in the community as people tried to get information.
Hundreds have been left homeless by the blaze, putting more pressure on officials in a city plagued by a chronic housing shortage. Numerous displaced are living in churches and community centres.
Construction began on the Grenfell Tower in the early 1970s, during the tenure of Edward Heath's Conservative Party government.
The statement comes as Transport for London partially closed two Tube lines because of London Fire Brigade (LFB) saying there was a "short-term risk of some debris falling on to the tracks".