Theresa May branded the support for Grenfell Tower families in the immediate aftermath of the fire as "not good enough", with police revealing that 58 people are missing and presumed dead.
The Prime Minister said there had been "huge frustrations" on the ground as people struggled to find information.
She added: "The response of the emergency services, NHS and the community has been heroic.
"But, frankly, the support on the ground for families who needed help or basic information in the initial hours after this appalling disaster was not good enough."
It came after she met victims of the blaze at Downing Street, amid criticism she had not seen them in the immediate wake of the disaster.
Metropolitan Police Commander Stuart Cundy warned that the death toll could rise further as he formally identified a first victim as 23-year-old Syrian refugee Mohammad Alhajali.
Of the 58, he said 30 were confirmed dead. Sixteen bodies have been taken to the mortuary including one person who died in hospital - the others have been recovered from the building.
Mr Cundy said: "Sadly, at this time there are 58 people who we have been told were in the Grenfell Tower on the night that are missing, and therefore sadly, I have to assume that they are dead."
"That number 58 may change. I really hope it won't, but it may increase."
Mr Cundy added: "My commitment to families is that as soon as we can, we will locate and recover their loved ones.
"The reason we had to pause the search and recovery yesterday was for the safety of our staff.
"We do not want another fatality arising out of this tragedy."
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".
When asked about the search, he replied that the officers had gone "all the way to the top" of the tower, and explained that the first phase was a visual search.
He also appealed to anyone who may have escaped from the building, but has not yet come forward, to make themselves known.
Mr Cundy said the police investigation into the blaze would look at the building and its refurbishment in 2016 and vowed to prosecute people if there was evidence.
The police are appealing to anyone with pictures or videos of the blaze to hand them in, as they may help establish not only where and how the fire started, but also how it spread.
Victims made clear their demands to Mrs May in the two-and-a-half hour meeting in Number 10.
A man representing the group, who did not give his name, told reporters they would make a full statement "in the community ".
He said the group had spoken about their "demands and what we expect".
Mrs May said she had fixed a deadline of three weeks for everybody affected to be rehoused locally.
She added: "I have ordered that more staff be deployed across the area, wearing high visibility clothing, so they can easily be found, dispense advice and ensure the right support is provided."
Family liaison officers are working with 52 families, and as soon as victims are identified, their loved ones will be told.
Mr Cundy said: "I absolutely understand the frustration of why figures haven't been released earlier. The reason for that - at one point, in terms of our casualty bureau, there were 400 people who were reported missing from Grenfell Tower.
"Grenfell Tower itself is 120 flats. We have worked tirelessly over the last four days to truly understand those that we know were there on the night."
Anger flared in the Kensington community over the weekend - with many protests taking place across the capital - as some accused the authorities of withholding information and responding inadequately.
Mr Cundy said: "The investigation will be exhaustive. My intention is that it will help provide answers.
"If, as we investigate, we identify issues that are a risk to public safety, we will not be waiting until the end of the investigation before we provide that information to the appropriate authorities.
"If there are any safety issues that we and experts that we will be using identify, we will share that immediately."
More than £3 million has been raised for the victims of the fire, while Downing Street has pledged a £5 million fund for emergency supplies, food and clothing for victims amid concerns the death toll will rise, with more than 70 people in total still believed to be unaccounted for.