"Donald Trump has done the absolutely worst possible thing you can do as an American political leader, and that's declare war on the faith itself," Graham told CNBC's "Squawk Box."
In the wake of jihadist terrorist massacres in San Bernardino and Paris, Trump on Monday said all Muslims without American citizenship should be temporarily barred from entering the U.S.
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"Donald Trump, by banning Muslims or suggesting we should do that, makes it very difficult to have partnerships with people in the faith who overwhelmingly reject the ideology," Graham said. "My plan is to get people within the faith who reject ISIL … to rally [and] create an army where 90 percent of the forces going on the ground with them to destroy a common enemy."
Recent attacks, including the Nov. 13 assaults in Paris, were carried out by terrorists linked to Islamic State, also known as ISIS and ISIL.