Sadiq Khan has put rent controls at the heart of his campaign to be re-elected as London mayor.
The Labour candidate vowed to push Prime Minister Boris Johnson to give him the power to limit the amount landlords can charge tenants.
Mr Khan said he had "massively increased" affordable homes in London but wanted more time to meet the housing targets he set himself in 2016.
His Tory rival Shaun Bailey said rent controls always led to higher rents.
The election for mayor of London takes place on 7 May.
Speaking at his campaign launch at a housing estate in Hackney, east London. Mr Khan claimed that during his four years in office, he had "massively increased the amount of council homes and genuinely affordable homes being built in London".
He added in the past two years, the highest number of genuinely affordable homes were being built since the mayor was given responsibility for housing and that more council homes than in any year since 1984 had started to be built.
Mr Khan said he had been frustrated that he had been blocked from making private rent more affordable which was why he was making the election a referendum on rent control.
"If Londoner's re-elect me as their mayor, I want there to be no doubt that it represents a clear and compelling mandate for their introduction.
"The prime minister will have to give us the powers we need because if he declines to do so, he'll be denying the democratic will of millions people who are crying out for help.
"And as we've all heard Boris Johnson repeatedly say himself, the democratic will of the people must be respected."
He made one reference to crime and transport said BBC London's political editor Tim Donovan.
Amina Gichinga from London Renters Union said rent controls were "urgently needed to help end the way that sky-high rents are driving people out from their communities and into poverty".
She called for him to mandate rent controls so that eventually no-one would have to pay more than a third of their income on rent.
But the Residential Landlords Association and the National Landlords Association called the policy "disastrous" for tenants.
Conservative candidate Shaun Bailey accused the mayor of "chasing quick headlines" rather than "doing his day job".
"This idea has failed around the world where it has been tried, leading to higher rents and longer waiting lists," Mr Bailey said.
Liberal Democrat candidate Siobhan Benita wants to bring thousands of empty homes back into use and build more homes for rent on Transport for London-owned land, as well as making London a legal, regulated cannabis market to tackle gangs.
Green Party candidate Sian Berry has promised to freeze rents and introduce a single transport fare across London.
Rory Stewart, who quit the Conservative Party and stood down as an MP to run for mayor, has vowed to set up a Mayor's Building Company to build hundreds of thousands of new homes.