Nihad Awad, executive director of the Council on American-Islamic Relations, also called for unity and urged politicians not to "exploit" the slaughter in Orlando, which left 50 dead and dozens more injured.
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"This is a hate crime. Plain and simple. We condemn it in the strongest possible terms," Awad told a news conference.
"It violates our principles as Americans and as Muslims. Let me be clear, we have no tolerance for extremism of any kind."
The FBI said the American gunman, 29-year-old Omar Mateen, who died in an exchange of fire with police, was believed to have made a 911 call pledging allegiance to IS before the shooting.
Awad referenced such reporting and said he had a word for IS members and supporters.
"You do not speak for us. You do not represent us. You are an aberration, you are an outlaw ... they don't speak for our faith. They never belonged to this beautiful faith."
With the 2016 race for the White House in full swing, Awad warned that perpetrators of attacks such as the one in Orlando "mean only to divide us" and called for calm on the political front.
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"And to those politicians who may try to exploit this tragedy, we ask them to respect the victims and their families. This is not the time to score points. This is not the time to exploit fear. This is the time for unity and faith."
White House hopeful Donald Trump lost no time in claiming the killing showed he has been right about Islamic extremism all long.
The Republican flag-bearer demanded that President Barack Obama stand down if he refused to blame the attack on what Trump called "radical Islam."
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The billionaire has previously argued that incidents like last year's San Bernardino shooting show that the United States should ban Muslim travelers.
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