"It is really important that we are clear about the scale of the challenge facing us as our teams search Grenfell Tower to recover those people still inside and return them to their loved ones", he said in a statement.
Speculation has focused on the role that cladding apparently used in a recent refurbishment of the tower may have played in the fire.
Grief turned to outrage Friday over a deadly high-rise tower fire in London amid reports that materials used in the building's renovation could have fueled the inferno that left dozens dead and missing as it decimated the public housing block.
In his Times column, Parris said every move May makes will be scrutinised "for further confirmation of the flaws we think we've spotted". Police barred their way and scuffles broke out, a reporter said. A public inquiry could take place before the inquests.
The meeting comes amid criticism levelled at the Prime Minister for not meeting those caught up in the fire in the immediate wake of the tragedy which killed at least 30 people, with the figure expected to rise.
Additionally, there is no Tube service between Edgware Road and Hammersmith "due to the recent fire in the Latimer Road area".
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.
Matthew Parris, a columnist and former Conservative lawmaker, said May's response to the fire had shown a lack of judgment which made her unsuitable to be prime minister.
She said firefighters did not know "why the fire spread in that absolutely unusual and extraordinary way".
Having visited residents and volunteers near the tower on Friday with her grandson William, the queen also led a minute's silence in Buckingham Palace on Saturday.
The area surrounding the council-owned tower has been plastered by desperate relatives with pictures of the missing, from grandparents to young children.
Police have said the recovery process could take weeks, and warned some of the bodies may be too burned to be identified.
Using drones and sniffer dogs, firefighters continued yesterday to search the burned-out hulk that looms over Notting Dale, a low-income community next to the super-affluent Notting Hill neighborhood in west London.
"We are not stupid, we're aware people are dead".
"They told me that this is not a matter for the council but for the coroner, the police and others", the crowd were told.
NHS England says the injured are being treated in four London hospitals.
Panoramic footage shows a flat littered with piles of debris, coated in black and grey ash - it is one of the few rooms safe enough for specialist crews to access following the blaze, which took hold in the early hours of Wednesday and has claimed at least 58 lives.
One of the victims was named as Mohammed Alhajali, a 23-year-old Syrian refugee, who came to Britain in 2014 with his brother.
British press is reporting that as many as 70 people are still missing and unaccounted for in the tower.
Despite that outcome, fire experts say "stay put" is still the best advice - as long as the building has proper fire-suppression protections, such as multiple stairwells, sprinkler systems, fireproof doors and flame-resistant construction materials, some of which were lacking in the London blaze. Officials and UK Chancellor Philip Hammond have indicated that the external rain-screen cladding believed to be the cause of the rapid spread of the fire at the Grenfell Tower may have been banned under building regulations in the UK.