"Our thoughts are with everyone affected by the fire at Grenfell Tower in London and our colleagues from London Fire Brigade and all the emergency services working in hard conditions to deal with this tragic incident", she said.
The number of confirmed fatalities from Wednesday's inferno in a West London residential block is now 17, British police have said.
Commander Stuart Cundy of the Metropolitan police said the absolute priority was retrieving bodies and identifying the dead, as part of an ongoing investigation carried out with the fire service.
Theresa May has ordered a public inquiry into the fire at a block of flats in west London on Wednesday morning which has killed at least 17 people, with many more still unaccounted for.
In a TV interview following her visit, Mrs May was told that some residents wished she had spoken to them as well as firefighters and had gone to see the community centres where local people are offering support to those affected.
She said the trio had initially followed the official guidance to stay put - but firefighters told them to flee around 90 minutes later.
Queen Elizabeth II and Prince Philip have paid tribute to London firefighters whose bravery prevented a greater loss of life in the high-rise fire.
The blaze has led to outrage after repeated alleged oversights in fire safety with residents saying they had warned authorities for years that the flats would be potential death traps if a blaze broke out.
The government department in charge of regulating building work - the Department for Communities and Local Government - did not respond to Reuters' questions, including whether such fire barriers were required by law.
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Fire Commissioner Dany Cotton says specialist dogs would start searching the 24-story building.
Meanwhile, the only Turkish family living in Grenfell Tower escaped with minor injuries and are now receiving medical treatment.
London's fire chief said it's not expected there'll be any more survivors, raising grim questions about the final death toll.
An investigation into the cause of the blaze is underway but the shock at its scale turned to anger and recriminations on Thursday.
The senior officer said that 5,000 missing persons calls had been made to the police casualty bureau, many involving multiple reports concerning one individual; one person was reported missing 46 times.
Asked by a seven-year-old boy at the scene "How many children died?", mayor of London Sadiq Khan replied: "The bad news, I'm afraid, is lots of people died in the fire". And entire families are missing after the deadly incident.
"Tragically now we are not expecting to find anyone else alive".
People light candles as they observe a vigil outside Notting Hill Methodist Church following the blaze at Grenfell Tower, a residential tower block in west London on June 15, 2017.
As of Thursday afternoon, more than 30 people were still being treated in hospital. "We owe that to the families, to the people who have lost loved ones, friends and their homes in which they lived".
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