The police are also considering manslaughter charges following the fire; seventy-nine people are confirmed dead, missing, or presumed dead after the blaze ripped through 150 flats in the Kensington building.
McCormack confirmed that a fridge-freezer started the fire at Grenfell Tower, and that it was not deliberate.
From initial "small-scale" tests, McCormack said both tiles and insulation used on the building did not meet expected standards.
Officials say cladding samples from 11 other high-rise buildings in eight municipalities in the United Kingdom, including in London, have also failed tests.
Detective Superintendent Fiona McCormack told reporters that "we are looking at every criminal offense from manslaughter onwards".
"It's not automatic that the building will be declared unsafe - otherwise we would just do it straightaway", the spokeswoman said.
Ms Constance said: "This week, we asked local authorities to give us further information about their high-rise domestic buildings".
Windhoek-Speaker of the National Assembly Professor Peter Katjavivi has sent a message of condolence to the families of the victims who lost their lives in the fire that destroyed Grenfell Tower in London on June 14, which claimed 79 lives.
"We are not interested in people's reasons for not telling us sooner and as the mayor has already said, people should be not be nervous about contacting us".
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She went on: 'I do not want there to be any victims of this tragedy that we do not know about.
Some 21 of the council's 24 tower blocks have metal cladding.
They were also concerned about the fridge freezer which malfunctioned and triggered the blaze - they had established with its manufacturer Hotpoint that it had never been subject to a product recall.
In total, tests for 600 high-rise buildings have been ordered by the British government.
An estimated 600 high rise buildings in England have similar flammable cladding to Grenfell tower.
Ms McCormack said: "Every complete body has been removed from the building".
"I feel really, really sick because of it", she said.
'There is a awful reality that we may not find or identify everyone who died due to the intense heat, ' she said, revealing the scale of the devastation.
"Such is that devastation down at the scene, this may take at least until the end of the year", Detective Superintendent McCormack said, adding, "There is the awful reality that we may not find or identify all those that died during the fire".