Metropolitan Police Commander Stuart Cundy told a press conference Monday that only five victims have been formally identified so far, and the death toll may change.
"Sadly for many families they have lost more than one family member," said Cundy, who added that the "painstaking" search and recovery operation is proceeding as quickly as possible, but may take "many many weeks."
Cundy explained that one of the reasons identification has been so difficult is because dental records are needed from victims who hailed from different countries around the world.
However, five people who were originally reported as missing have since been found safe and well.
Police chief: Nothing could have prepared me
The police chief, who went inside the charred shell of the high-rise tower over the weekend, told reporters: "I've investigated major crime for most of my service and I've seen some terrible things but I don't think anything prepared me for what I was going to see when I was in there."
The government has promised a public inquiry,
and police have opened a criminal investigation.
Cundy said the "complex" and "exhaustive" inquiry will focus on a range of issues including how the building was constructed, a recent refurbishment of it, how it is managed and maintained and fire safety measures.
Speculation has focused on the role that cladding apparently used in a recent refurbishment of the tower may have played in the fire.
A senior UK government minister said Sunday that he believed the cladding is banned in Britain
for buildings above a certain height.
"My understanding is the cladding in question, this flammable cladding which is banned in Europe and the US, is also banned here," Chancellor of the Exchequer Philip Hammond told the BBC's "The Andrew Marr Show."
"So there are two separate questions. One, are our regulations correct, do they permit the right kind of materials and ban the wrong kind of materials? The second question is were they correctly complied with?"
Hammond said that will be a focus of the inquiry and investigation.
Rydon, the company that carried out the recent refurbishment, said the "project met all required building regulations."
Authorities have also faced questions about why the block, built in the 1970s and home to 125 families, was never fitted with a sprinkler system that might have saved lives.
"I would like to reassure everybody that we will be looking at all criminal offenses that may have been committed by any individual or any organization," said Cundy.
Britain remembers victims
Britain observed a moment of silence at 11 a.m. Monday in remembrance of the victims. It was joined by firefighters from stations across the country.
A vigil was held in Parliament Square in central London Monday evening.
Conservative Prime Minister Theresa May has announced a fund of £5 million ($6.4 million) to help those affected by the blaze.
May has faced criticism for failing to meet survivors in the immediate aftermath of the disaster.
On Saturday, when she did meet residents, she said the response to the fire had been "not good enough."
On Monday, when asked if the Prime Minister thought her own response was good enough, a Downing Street spokesperson replied: "The Prime Minister has a job to do. You heard ministers talking over the weekend, who are always in close contact with her. She was focused on making sure there was a taskforce up and running, getting that done. "