Most Helpful Girl
They've been doing that. It hasn't gotten much attention and media coverage, but after the Florida attack especially they got together several of the major Muslim groups in the country, and the leaders went on TV live to condemn the act. They've done that after other attacks too, and always issue statements to express sorrow for the victims and disgust with ISIS.
There are also Muslim groups actively engaging with the public to show them they value the same things we do, aren't in any way supportive of ISIS, etc. They've protested against ISIS in the streets, and been on social media making anti-ISIS groups, and posting stuff against them.
There's only so much you can do, though. Also, from their point of view what ISIS is doing is so far away and deranged from what they believe in, that they don't identify with them at all, and that's why they say ISIS followers just aren't Muslims and aren't true believers in Islam. It's a bit like what Christians did when the Westboro Baptist Church was protesting soldier's funerals and holding up "God hates fags" signs - Christians mostly condemned them and said that's not what Christianity is about, and they aren't true Christians. That's what people in the Muslim community are doing too, but to a much greater extent.1
Most Helpful Guy
They should, the Islamic community is the best party to help us fight terrorism.
Reason: they have the largest chance of being able to influence the behavior of potential terrorists.
And they should also strongly advise people within their community not to provide any form of support to extremists.
We see here in Belgium that many extremists were able to hide for a long time, thanks to support from the community they lived in.1