Research from the Greater London Authority and YouGov estimated 500,000 private renters in London were potentially facing eviction.
The government's temporary ban on evictions ends on Sunday.
It said it had taken "unprecedented action to support renters by banning evictions for six months".
Mr Khan urged the government to give him powers to freeze rent to prevent a "tsunami of evictions".
He has said during this two-year freeze, rents would be allowed to fall but not rise and that landlords would not be able to charge new tenants a higher rate than previous ones.
The mayor is also asking for grants to allow renters to stay in their homes to clear arrears and to scrap "no fault" evictions as well as expanding access to welfare by scrapping the Benefit Cap.
"More than ever, Covid-19 means that many of London's private renters are facing a really uncertain future," he said.
"More likely to be in lower-paid and insecure work, the end of the furlough scheme means even more renters in the capital are now at risk of pay cuts or losing their job."
He added: "If Berlin can freeze rents for five years, there's no reason London shouldn't be able to freeze rents for two years in these extraordinary times."
Alicia Kennedy, director at Generation Rent, said: "Evictions have been paused, but that hasn't stopped some London landlords from raising the rent, which can force a tenant to leave their home."
She said tenants had contacted the company to say they had been hit with a rent increase after telling their landlord their income had been affected by the pandemic.
Chris Norris, Policy Director for the National Residential Landlords Association, said rent controls would be a disaster for anyone looking for somewhere to rent.
"All they would do is drive landlords out of the market exacerbating an already serious shortage of homes available.
"Rather than driving a wedge between landlords and tenants the Mayor should focus on using the powers he already has to boost the supply of available housing, including for private rent."
The Ministry of Housing, Communities and Local Government said it had recently changed the law to increase notice periods to six months to help keep people in their homes over the winter months.
"These measures strike a balance between protecting vulnerable renters and ensuring landlords whose tenants have behaved in illegal or anti-social ways have access to justice."
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