Mental health campaigners say that papers used to make hand-rolled cigarettes should carry printed warnings about the dangers of cannabis.
Cannabis is often smoked in hand-rolled cigarettes
Rethink's efforts have been directed at Imperial Tobacco, which makes the UK's best selling brand, Rizla.
Cannabis has been linked to mental health problems, and Rethink said the messages could help target users.
Imperial said it did not endorse drug use, and stressed it followed legal requirements on warnings.
While both cigarette packets and the packaging for loose rolling tobacco have carried prominent public health warnings for some years, these rules do not currently cover cigarette rolling papers.
However, Jane Harris, Rethink's head of campaigns, accused the makers of Rizla of "being irresponsible".
She pointed to the results of a survey which suggested that many members of the public associated the product more with cannabis use than tobacco smoking.
She said: "Health warnings work: 12% of people quit smoking as a result of warnings on cigarette packets."
She also called on the government to carry out more education on the health effects of cannabis, in particular the increased risk of psychosis linked to the drug.
"Our research shows that young people want this information - we think they should receive it as a right."
Amanda Sandford, from the group Action on Smoking and Health, said that she wanted to see health warnings about smoking tobacco on rolling paper packets.
She said: "There are warnings on loose tobacco packets, but once they are opened, we think these don't have the same impact as the messages on cigarette packets."
A spokesman for Imperial Tobacco said: "We don't endorse the illegal use of cannabis using any of our products, and we meet all the legal requirements with regard to packaging."