"Sadly, I can confirm that the number of people that have died is now 17", London police commander Stuart Cundy told reporters.
Some 19 patients are still being treated in hospital, of whom 10 are in a critical condition, the National Health Service said.
Experts said the intensity of the fire that raged for hours at the 24-story building will make naming victims an extremely hard and slow process.
In a television interview, she sidestepped questions over whether she had misread the public mood.
On a day when thousands of people took to the streets to demand answers and justice over the deadly blaze, the Labour leader said ministers had a duty to stick to their guarantee, but officials attempting to find places for those displaced gave the impression of being overwhelmed. In a statement to mark the official celebration of her 91st birthday, she said: "It is hard to escape a very soreer national mood" after a "succession of terrific tragedies".More news: Portugal and Mexico draw 2-2 in Confederations Cup
Her message concluded: "Put to the test, the United Kingdom has been resolute in the face of adversity".
Frustration has been mounting in recent days as information about those still missing in the blaze has been scanty and efforts to find temporary housing for the hundreds of now-homeless tower residents have faltered.
A crowd of furious protesters stormed Kensington town hall demanding answers from the local authority before marching to the base of the tower. The Home Office says it will make arrangements for the family of Mohammad Alhajali to "travel to the U.K.in these terribly sad circumstances".
Engineering experts and fire safety specialists believe the building's exterior cladding may have quickly fueled the blaze, overwhelming fire protection devices.
Sixteen "very ordinary people" sat in Downing Street to bring their concerns to Theresa May in an "unprecedented" meeting and finally felt they were listened to, the Bishop of Kensington, Dr Graham Tomlin said. British officials have ordered a review of other buildings that have had similar renovations.
Residents affected by the Grenfell Tower atrocity were passionate and angry during a lengthy exchange with the Prime Minister, a bishop who sat with them revealed.More news: Portugal forest fire victims die in their cars as flames engulf road
The tragedy has provoked a huge response from nearby communities.
May who has promised $6.4 million for emergency supplies, food and clothing, has also announced a judge-led inquiry into the disaster.
Some Grenfell residents had warned months ago that fire safety issues at the tower left it at risk of a "catastrophic" event.
A fire department spokesman said crews are working to secure the debris so that two subway lines could be reopened as soon as possible.
British officials say they are helping the Syrian family of the first officially confirmed victim of the London tower blaze to come to Britain.More news: Another police shooting acquittal worries black gun owners
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