"I am not going to demonize and demagogue and declare war on an entire religion. That's just plain dangerous, and it plays into ISIS's hand," Clinton, the presumptive Democratic presidential nominee, said on NBC's "Today" show Monday morning, referring to the Islamic State in Iraq and Syria.
"I think Trump, as usual, is obsessed with name-calling," Clinton added.
"From my perspective, it matters what we do, not what we say. It matters that we got bin Laden, not what name we called him, but if he is somehow suggesting I don't call this for what it is, he hasn't been listening."
Clinton said the U.S. is facing terrorist enemies "that use Islam to justify slaughtering innocent people."
"We have to stop them, and we will. We have to defeat radical Jihadist terrorism, and we will," she said.
"To me, radical jihadism, radical Islamism, I think they mean the same thing. I'm happy to say either, but that's not the point. All this talk and demagoguery and rhetoric is not going to solve the problem."
Trump, the presumptive GOP presidential nominee, on Sunday said President Obama should resign from office and suggested Clinton should drop her White House bid over the issue.
"If Hillary Clinton, after this attack, still cannot say the two words 'Radical Islam' she should get out of this race for the Presidency,” Trump said in a statement on Sunday.
The nightclub attack Sunday morning left 49 people dead and many more wounded. ISIS took credit for the shooting, which Obama called an "act of terror."