Ramesh Kallidai of the Hindu Forum of Britain said the swastika had been a symbol of peace for thousands of years before the Nazis adopted it.
He said a ban on the symbol would discriminate against Hindus.
Germany, holder of the EU presidency, wants to make Holocaust denial and the display of Nazi symbols a crime.
Mr Kallidai said his organisation was writing to European lawmakers to highlight the issue.
Hindu groups in Holland, Belgium and Italy were also involved in the campaign, he said.
“The swastika has been around for 5,000 years as a symbol of peace,” he said. “This is exactly the opposite of how it was used by Hitler.”
He said that while the Nazi implications of the symbol should be condemned, people should respect the Hindu use of the swastika.
“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.”
The group said banning the swastika was equivalent to banning the cross simply because the Ku Klux Klan had used burning crosses.
The swastika is already banned in Germany. A previous attempt to ban it across the EU in early 2005 failed after objections from several governments, including the British.
Germany took over the six-month EU presidency on 1 January.
We appreciate your support
One way in which you can support us — at no additional cost to you — is by shopping at Amazon.com.
Our website includes affiliate links, which means we get a small commission — at no additional cost to you — for each qualifying purpose. For instance, as an Amazon Associate Religion News Blog earns from qualifying purchases. That is one reason why we can provide this service free of charge.