London Fire Brigade chief Dany Cotton said there had been "a number of fatalities" in what she called an "unprecedented" blaze.
"I cannot confirm the number at this time due to the size and complexity of this building," she told reporters at the scene in west London.
"This is an unprecedented incident. In my 29 years of being a firefighter, I have never ever seen anything of this scale," she said.
The ambulance service said 50 people had been hospitalised.
Witnesses said they had seen some people fall or jump from the stricken Grenfell Tower and at least one resident waving a piece of white cloth from one of the upper floors as flames ravaged the building.
The alarm was raised just before 1:00 am (0000 GMT) and within an hour flames had engulfed the entire block, which contains 120 flats.
Residents said the fire was on the exterior of the tower, which had been covered in cladding in a major refurbishment completed last year.
Nearly 10 hours on, flames could still be seen inside the charred building as a thick, black smoke filled the sky.
London Mayor Sadiq Khan said firefighters were only able to reach the 12th floor at the height of the blaze during the night.
"A lot of people are unaccounted for," he told Sky News television.
Cotton said the building's structural integrity was being monitored and it was stable enough for fire crews to work inside.
"We rescued a large number of people from inside the building very early on," she said, adding that she had spoken to firefighters who had reached the 19th and 20th floors.
"We are making steady progress."
Large pieces of debris could be seen falling from the building, a 1970s local authority-built block in the working-class north Kensington area.