The call came after a meeting with 20 Muslim leaders on Thursday to discuss relations between their community and the rest of the borough in what the mayor called 'tense and even frightening times'.
Deputy speaker Muhammad Khan said Bedford had a good record as a multi-racial community and Muslims were concerned to keep it that way, but the habit of some newspapers of referring to 'Islamic terrorists' was harmful.
Other leaders said there was no evidence of extremist groups such as the Muhajiroun, subject of a BBC probe on Wednesday, existing in Bedford.
The leaders also agreed that if the BNP fought a for seat in the June 10 Euro parliament, their community should not react to provocation.
The group decided that there should be a meeting every six months to keep an eye on the situation and that young Muslims should be invited too.