Rogers was speaking at the launch of London Open City - an exhibition from the London mayor's urban design studio Design for London, directed by Peter Bishop - at Somerset House.
Rogers said: "London is the greatest city of today. Five years ago London had the worst open spaces in the world. Now it has quality trees and street furniture, but it still has a long way to go."
He added: "Everyone has a right of access to open public space. There should be a legal right created for this, just as there is for health care. Public space is much more important than buildings.
"There should be a right for all of us to have a bench within 100m and a tree within view from our houses, as well as a play space within 300m-400m.
"There should also be a law that ensures you have easy access to a bus taking you to a big park. And every borough should have a public domain plan - not only displaying what exists but what the borough aspires to become."
The exhibition "suggests an approach to unlocking the potential of London's public spaces and streets" to make them easier and more enjoyable to use. But Landscape Institute president Nigel Thorne said he was "frustrated" that landscape architects had not been consulted and that the development was "not collaborative".
The London Open City exhibition is on until 27 April.