Release said the 'Nice people take drugs' strapline was intended to spark "a realistic and honest" debate on government's policies towards drug use in the UK.
The ads appeared outside and inside of a number of buses in London last week before CBS Outdoor scrapped the campaign after a complaint by one of the bus companies.
After the complaint, CBS Outdoor asked the Committee of Advertising Practice (Cap) how to proceed, and was told that the ads indeed could be seen as offensive.
However, Cap did not advise CBS Outdoor to take down the ads, nor has the campaign received complaints from members of the public.
CBS Outdoor pulled the plug on the campaign and suggested Release change the wording on the ads to include the words "also" or "too" to insure minimal offence to the general public.
Sebastian Saville, chief executive of Release, told the Guardian he was "deeply concerned" about CBS Outdoor's decision to remove the ads.
Saville said: "The 'Nice People Take Drugs' campaign is about getting people to think about drug use in our society and for politicians to stop being so frightened of having an open debate on how to more effectively deal with the current situation."
A CBS Outdoor spokesman said the inclusion of the campaign was an "oversight" and the company should have briefed Cap before running the ads.
The media owner said Release can re-run the campaign free of charge at the end of the month if the wording is changed.
Saville said Release is currently working on a new slogan.