Under existing legislation parties on all sides of the political spectrum are allowed to visit schools to take part in debates and explain their policies.
The current law does not allow schools to discriminate between parties because of their opinions. Björklund has previously said that the education department will conduct a review of its regulations.
"I think we are all in agreement that this idea of allowing obvious Nazi parties to get access to our youth shouldn't happen," Björklund told Sveriges Radio Ekot programme.
He is now calling for all political parties in the Rikstag to consider changing the law. Björklund added that he is going to reach out to senior members of the parties in a personal capacity to get talks started regarding this issue.
"It is very desirable that there is a broad political consensus on these types of rules which are the foundation of our democracy," he said.
The Swedish Teachers' Union (Lärarförbundet) they said welcomed the proposal put forward by the Education Minister.
"I think it's gratifying and a great success that Björklund is finally listening to teachers and schools. Schools should not be a playground for Nazi propaganda," Eva-Lis Sirén, chairperson of the Teachers' Union, told Aftonbladet.