Cundy explained that one of the reasons identification has been so hard is because dental records are needed from victims who hailed from different countries around the world.
Facing fierce criticism over its response to London high-rise inferno, the British government has sent its staff to assist local council authorities in rehabilitation of victims of the deadly blaze that claimed at least 58 lives and rendered hundreds homeless.
Cundy said there may have been people in the tower that police are not aware of, which would add to the death toll.
Cundy said police will investigate the tower's refurbishment project, which experts believe may have left the building more vulnerable to a catastrophic blaze.
"This is an incredibly distressing time for families and they have my commitment that we will do this as quickly as we possibly can", he said.
Alongside both police and fire investigations into the blaze, she has promised to set up a public inquiry, Reuters news agency reported. "Where offences have been committed, I will do everything in my gift to make sure they are brought to justice", he said.
"I have always said I will be accurate about what I know, so the next figure of those presumed dead and missing will be released tomorrow, Monday 19 June".
"The terrible reality is, as I've said before, is that due to the intensity of the fire and the devastation within Grenfell Tower that we may not be able to identify everybody that died", he said. "We will continue to look at what more needs to be done", Mrs May said in a statement issued by her office.
"Our focus has been on those that we know were in Grenfell Tower".
The National Health Service said that 17 patients were still being treated in hospital, of whom nine remain in critical condition.
"The tragedy at Grenfell Tower has left a number of local people in need of urgent assistance", a spokesman for the three royals at Kensington Palace said.
The images, captured by a specialist police recovery team working alongside colleagues from the London Ambulance Service and the London Fire Brigade, show homes completely destroyed, with deep layers of ash and charred rubble covering the floors.
Sixteen bodies have been taken to a mortuary for examination. Many questions also center on the speed at which the fire spread.