She said: "Today is a traditional day of celebration".
At least 58 people are dead or presumed dead after the blaze.
Twenty-four people are still in the hospital, 12 of them in critical condition. Police barred their way and scuffles broke out, a reporter said.
"It is hard to escape a very sombre national mood", the queen said in a statement to mark her official birthday - an occasion that typically does not result in any public comments from the monarch.
Kensington and Chelsea Town Hall became another flashpoint on Friday with protesters storming the building, accusing authorities of ignoring them and of forcing low-income families to live in sub-standard housing.
Opposition Labour leader Jeremy Corbyn, London mayor Sadiq Khan, Prince William and Queen Elizabeth, 91, have all visited the local area and anger has been growing in the community.
The cause of the fire is still unknown but "there is nothing to suggest the fire was started deliberately", London police said in a Friday statement.
The meeting is unlikely to quell complaints that May has been slow to reach out to victims, despite her announcement of a $6.4m emergency fund to help the displaced families. During the video, Rania is seen leading people in the smoke-filled corridor into her apartment for shelter to ensure their safety.
A woman, who wiped away tears of frustration as she moved away from St Clement's Church, said: "Everyone has lost everything and no one is doing nothing".
Rain-softened Erin Hills provides daunting weekend challenge
Open and British Open and the third at the PGA Championship. "As long as it's a good tournament, it's good for the U.S. Open on Saturday, but Brian Harman stole some of that thunder by taking the lead through three rounds at Erin Hills.
"It will go to establish the answers of what happened in the fire and how it spread; it will look at the building itself; it will look at the refurbishment as well".
Prior to the meeting with victims, other residents of the block and volunteer workers, she chaired a meeting of a government task force on the disaster. More than 3 million pounds ($3.8 million) have been raised for the victims. Everybody is. It's not to say it is unfair on us but I mean, we were put in a situation.
Metropolitan Police said family liaison officers have been deployed to support 52 families of residents who died, were injured or were reported missing. But in an interview about the fire, May ducked the questions.
She said earlier that the national mood is somber but that Britain is resolute in the face of adversity. This year, however, it is very hard to escape a very sombre national mood.
Protesters storm Kensington Town Hall in anger at the Grenfell Tower tragedy.
A firefighter who battled an intense blaze devouring a 24-storey apartment building in London has been left wishing he did more.
"We have colleagues in there as we speak, searching for and recovering those that have died".
Some Grenfell residents had warned months ago that fire safety issues at the tower left it at risk of a "catastrophic" event.
He said: "Clearly it's quite unprecedented for 16 very ordinary people, who this time last week were walking their dogs or talking to each other in the streets around here and north Kensington, actually to be in 10 Downing Street talking face-to-face with the Prime Minister".
Comments