Only five victims have been formally identified - and Cundy said that because of the fire's intensity and the devastation it caused, authorities may not be able to identify everybody who died.
"Whilst I've said I think there may be changes, I don't think those changes will be as significant as the changes we've seen over the last few days", he said.
The minute's silence was held outside Caird Hall at 11am in line with others across the country following the blaze at Grenfell Tower last Wednesday.
The fire has prompted warnings about fire safety risks in many other council tower blocks built in the same era.
"The residents of Grenfell Tower, families who have lost loved ones, and the emergency services who have been working so hard to help them have been through some of the most harrowing and traumatic experiences imaginable", Mrs May said.
"There are 58 people who we have been told were in Grenfell Tower on the night that are missing and therefore, sadly, I have to assume that they are dead".
He said: "We must also prepare people for the awful reality that some people may not be identified due to the intensity of the fire".
Religious Leaders Hold Moment Of Silence For Victims Of London Van Attack
And the guy was shouting, basically he was saying, "it's our turn, this is for the people [that] you killed earlier". Several bunches of flowers had been deposited outside the mosque as commuters went to work on Monday morning.
Queen Elizabeth and Prince William visited the disaster site, which was compared to the visit of May, who confined herself to speaking to police and fire brigade officials and not the victims.
If that death toll is confirmed, it would make the Grenfell Tower blaze the deadliest in London since World War Two. "I really hope it won't, but it may increase", he said. "It does not matter why you have not told us, what is important is that we know you are safe".
"What we don't know at this time, and we won't know until the investigation concludes, is why the fire spread in that absolutely unusual and extraordinary way in that building", she said. "Wherever we can, we will bring people to justice if there is evidence".
"The Prime Minister is distraught about what has happened", said Green, who was appointed May's deputy in the wake of the general election.
"His family is being supported by liaison officers from the Metropolitan Police", Cundy said.
Cundy's latest statement came shortly after police released new images from inside the burnt-out building.
"Mohammed undertook a risky journey to flee war and death in Syria, only to meet it here in the United Kingdom, in his own home", the Syrian Solidarity Campaign said in a statement.
- Mexico's Hector Moreno scores late equaliser against Portugal at Confederations Cup
- Cairn tax dispute: IT dept confiscates dividend, refund
- Dividend Diamond in Focus Pitney Bowes Inc. (NYSE:PBI)
- L'Europe y voit une "substance extrêmement"
- US Supreme Court Backs Chevron In $9B Ecuador Pollution Case
- Queen Elizabeth to inaugurate new session of parliament June 21
- Ossoff, Handel race for House costs record $50 million
- Gatland drafts in reserves for Lions; Donald to lead Chiefs
- Presidential polls: Bihar Guv Ram Nath Kovind is NDA's surprise candidate
- Fed Raises Interest Rate by a quarter point