Sadiq Khan has warned Londoners there will be "a large number" of deaths from coronavirus and temporary mortuaries will be set up across the capital.
Just under 4,000 people in London have been infected with the virus, according to latest government figures.
At least 180 people in the capital have died from Covid-19 so far.
The Mayor of London said there was a specific group looking at mortuary planning.
His comments come as the Ministry of Defence continued to turn the ExCeL centre in east London into a Nightingale hospital to cope with the demand on the NHS.
"I need to warn people that it is going to a lot worse over the next few weeks," Mr Khan said.
"But we are going to do what we can for that eventuality. The number of people we are talking about are large and we need to be ready for that."
"You will have seen the amount of dead already in London, we are two or three weeks ahead of the rest of the country and we know the peak is coming soon, three to five weeks away."
A temporary mortuary has already been set up in the borough of Westminster and Mr Khan said "there will be more" across other parts of the capital.
He said: "Anyone watching the news and seeing what is happening around the world knows the number of deaths we are talking about."
Mr Khan described coronavirus as "an invisible killer" and said it was important Londoners did everything possible to stop the spread of infection.
Meanwhile, NHS chief executive Sir Simon Stevens said NHS staff would start being tested for coronavirus from next week, including critical care nurses, intensive care staff, ambulance workers and GPs.
Sir Simon said that as of Thursday, there were just under 3,000 empty and available hospital beds in London, and there would be additional beds next week at the new NHS Nightingale hospital at the ExCel.