But Mr Burnham said the housing crisis was “getting worse every year” because of it.
Speaking on Breakfast, he said: “We lose social homes every year, and across Greater Manchester for the last year 500 social homes were lost.
“I’m saying to Whitehall and Westminster – you need to allow us to suspend Right to Buy from the new homes that we are building because if we don’t, trying to solve the housing crisis is like trying to fill a bath but with the plug out because you try and build new homes but you lose them at the other end.”
Mr Burnham hoped to solve the housing crisis in Greater Manchester within a decade by calling on the government to suspend, “not end” Right to Buy.
It formed part of his pledge to build 10,000 homes across the county, with at least 1,000 in every borough.
By working with public bodies to “release brown field land”, he said the social homes would be a “new generation of council homes which will be cheaper to run”.
“There is no solution to the housing crisis without building homes that people can truly afford,” he added.
As part of his four-year term as mayor, Mr Burnham also wants to bring in a Greater Manchester Good Landlord charter to improve standards in the private rented sector.
He said: “We are going to give our residents the right to request a property check if they are concerned their home is unfit or unsafe.”
The mayor of Greater Manchester has the most powers of any elected mayor outside London and oversees decisions in relation to areas including public transport, strategic planning and housing, productivity and skills, economy and innovation, and the environment.
They also fulfil the role of police and crime commissioner as well as hold responsibility for Greater Manchester Fire and Rescue Service.