“We propose that 'Un-Islamic State' (UIS) could be an accurate and fair alternative name to describe this group and its agenda - and we will begin to call it that," the letter says.
Signatories to the letter include Sughra Ahmed, the president of the Islamic Society of Britain. Members of New Horizons in British Islam, the Association of British Muslims and the Association of Muslim Lawyers also signed the letter.
Using the group’s preferred name could help it radicalise yet more Britons, the signatories wrote.
“We need to work together and make sure that these fanatics don't get the propaganda that they feed off,” the letter says.
“This isn't going to fix the problem of some young people in our community being radicalised by extremists. There's more we need to do, together, to tackle that.
“But confronting this falsehood, that it's somehow 'Islamic' to go off to Iraq or Syria and murder people, is a step in the right direction.”
Security services believe as many as 500 Britons have gone to the Middle East to fight, and British politicians have raised fears about jihadis returning to Britain.
The letter was released just before Isis released a video claiming to have killed a British aid worker.
By Andrew Griffin