Hindus in Britain, the Netherlands, Belgium, France and Italy plan to visit each EU member state, European Commission leaders and members of the European Parliament to garner support for a pressure group intended to resist the German move.
Germany plans to use its presidency of the EU to launch an initiative which could lead to common laws across the bloc making it a crime to deny genocide and display Nazi symbols.
"The swastika has been around for 5,000 years as a symbol of peace. This is exactly the opposite of how it was used by Hitler," said Ramesh Kallidai of the Hindu Forum of Britain.
"It is almost like saying that the Klu Klux Klan used burning crosses to terrorize black men, so therefore let us ban the cross. How does that sound to you?"
The European umbrella group of Hindus plans to launch in the European Parliament in May.
The swastika, the symbol of Hitler's Nazi Party, is banned in Germany, which assumed the EU's six-month rotating presidency on January 1. In Hindu tradition, it is one of the religion's most sacred symbols of peace.
Germany, alarmed by a rise in far-right crime, wants to harmonize the rules for punishing offenders in member states.
"In Germany the fight against racism and xenophobia is both an historic duty and a current political concern," Germany's Justice Ministry said, laying out its plans earlier this month.
"Every time we see a swastika symbol in a Jewish cemetery, that of course must be condemned. But when the symbol is used in a Hindu wedding, people should learn to respect that," he told Reuters.
"In Sanskrit it means May Goodness Prevail. Just because Hitler misused the symbol, abused it and used it to propagate a reign of terror and racism and discrimination, it does not mean that its peaceful use should be banned."