(CNN) Hillary Clinton said Monday she's not afraid to say "radical" Islam as she countered attacks from Donald Trump that she's too politically correct to use the phrase.

"From my perspective, it matters what we do more than what we say," Clinton said on CNN's "New Day." "And it mattered we got bin Laden, not what name we called him. I have clearly said we -- whether you call it radical jihadism or radical Islamism, I'm happy to say either. I think they mean the same thing."

Clinton -- who also reupped her call to restore the assault weapons ban -- was forceful in dismissing Republicans' criticism -- vocally echoed by Trump -- that President Barack Obama and Democrats won't describe such terror attacks as "radical Islamic terrorism."

Clinton's comments went further than she has before in the language she uses to describe radical Islam and swiftly undercut one of Trump's central lines of attack against her regarding the fight against terrorism. Her interview Monday morning also notably separated the former Secretary of State from Obama's approach -- in his remarks from the White House on Sunday about the massacre, he never used the words "radical Islam" and he's made it a point not to do so in similar past domestic attacks.

Trump was also interviewed later on "New Day" Monday morning about the Orlando attack, and repeated the charge that Democrats' reluctance to say "radical Islamic terror" was hampering efforts to combat terror.

"The first thing you need is a president that will mention the problem. And he won't even mention what the problem is," Trump said. "Unless you're going to say that, you're never going to solve it."

Trump then claimed Clinton was "afraid to use [the term] because President Obama doesn't want her to" before host Christine Romans corrected him, pointing out Clinton had just used the term in the preceding interview. After Romans interjected, Trump replied, "She would love to use those words because almost everybody agrees that those words should be used."

In her appearance, Clinton also was quick to link the attack to the terror organization.

"This was a terrorist attack. ISIS appears to be claiming credit for it, whether it had anything to do with it or not -- at a minimum, they seem to have inspired it," Clinton told host Chris Cuomo.

And Clinton took a veiled swipe at Trump, who has proposed temporary banning Muslims from entering the United States, for targeting Muslims in his campaign rhetoric.

"What I won't do, because I think it is dangerous for our efforts to defeat this threat, is to demonize and demagogue and declare war on an entire religion," she said. "That plays right into ISIS' hands."

Clinton hit Trump by name, saying, "I think that Donald Trump's rhetoric is quite dangerous to our country."

The presumptive Republican nominee, citing the Orlando attack, also repeated his warning that Muslim communities aren't doing enough to self-police and report cases of extremism and radicalized individuals before attacks occur.

"The communities that we're talking about, they know about this guy. They knew that this was tremendous potential for blow up," Trump said.

"Right now we have thousands of people in the United State who have the same kind of hate in their heart as he had. And we have to know who they are," he added.

Trump also reiterated his opposition to accepting Syrian refugees, adding that terror problems "will only get worse."

Clinton, in her interview calling the aftermath of the attacks a "time for statesmanship, not partisanship," projected confidence in the United States' ability to defend against future terror attacks.

"We have the resources, relationships and experience to get it done," she said. "And this is a moment -- for Republicans, Democrats, independents -- for all Americans to work together as one team. It's time for statesmanship, not partisanship. Our fellow citizens should expect that."

And the presumptive Democratic presidential nominee made the case for stricter gun safety laws in the wake of the massacre, arguing that "common sense gun safety reform across our country would make a difference" while calling for the reinstatement of an assault weapons ban.

"We can't fall into the trap that is set up by the gun lobby that says if you can't stop every shooting in every incident you should not try to stop any. We did have an assault weapons ban for ten years. I think it should be reinstated," she said.

On the other hand, Trump said that if people in Pulse had been armed, the scope of the tragedy would have been lessened.

"If you had guns in that room, if you had -- even if you had a number of people having them strapped to their ankle or strapped to their waist, where bullets could have flown in the other direction right at him, you wouldn't have had the same kind of a tragedy," Trump said on CNN.

In a separate interview on Fox News' "Fox and Friends," also on Monday, Trump continued to criticize the Obama administration's anti-terror efforts and even hinted at some hidden motivation for Obama.

"We're led by a man who is very -- look, we're led by a man that either is not tough not smart, or he's got something else in mind. And the something else in mind, you know, people can't believe it. People cannot believe, they cannot believe that President Obama is acting the way he acts and he can't even mention the words radical Islamic terrorism. There's something going on. It's inconceivable. There's something going on," he said.