The move would make smoking heroin an offense on par with injecting it, which is illegal in Norway but tolerated.
Oslo's municipality already operates a site where heroin addicts can inject drugs under safer, more hygienic circumstances than they would have had access to otherwise.
"The number of fatal overdoses is too high and I would say it's shameful for Norway," Health Minister Jonas Gahr Stoere told daily Dagsavisen.
"The way addicts consume their drugs is central to the question of overdoses. My view is that we should allow people to smoke heroin since injecting it is more dangerous," he said.
Norway has one of Europe's highest death rates among drug addicts, with 30 percent of 262 fatal overdoses in 2011 coming from heroin, according to the Norwegian Institute for Alcohol and Drug Research, Sirus.
By comparison, 168 people died on Norwegian roads in the same year.
Stoere spoke six days before the presentation of a government plan for fighting drug addiction, and claimed to have the backing of a majority of the centre-left coalition.
"This isn't about some kind of legalization of heroin but about being realistic," he said.
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"Those who are in the unfortunate situation of injecting themselves in a (municipality) drug room should ... be able to inhale. It is less dangerous, you consume less and the risk of contracting a disease is lower," he added.
"It's a paradox that you can't smoke heroin when you can inject it, since the first method is less dangerous than the second," Sirus researcher Astrid Skretting said.
"But the culture of injecting (which provides a more immediate effect than smoking) seems deeply rooted in Norway and it's not certain that a decriminalization will lead to a radical change in behaviour," she added.