Trump, Clinton spar after Orlando massacre

Clinton, Trump clash in speeches after Orland... 01:56

ORLANDO -- The Orlando massacre has become part of the presidential campaign.

"The only reason the killer was an American in the first place was because we allowed his family to come here," said Donald Trump on Thursday.

Donald Trump speaks on deadly Orlando shootin... 33:28

Speaking in New Hampshire, Donald Trump argued the nation's very survival hinges on banning Muslim immigrants.

"If we don't get tough, and we don't get smart and fast, we're not going to have our country anymore," he said. "There will be nothing, absolutely nothing left."

His proposal has been denounced by Republican leaders. But that did not stop Trump, who argued "radical Islam" is incompatible with Western values.

"They enslave women and they murder gays," he said. "I don't want them in our country."

While Clinton said Thursday: "Our open diverse society is an asset in the struggle against terrorism not a liability."

In Cleveland, Clinton said scapegoating one religion makes America less safe.

"It's no coincidence that hate crimes against American Muslims and mosques have tripled after Paris and San Bernardino," she said. "That's wrong and it's also dangerous. It plays right into the terrorists' hands."

Clinton has long argued that using the term "radical Islam" also plays into terrorists hands.

But in interviews Monday, under pressure from Trump, she changed course.

"Whether you call it radical jihadism, radical Islamism, I think they mean the same thing, I'm happy to say either," she said.

Trump said repeatedly Monday that the president either doesn't know what he's doing or is intentionally going easy on terrorists. He never said why the president would do that, but this is the man who for years accused Mr. Obama of being a secret Muslim who was not born in this country.

  • Nancy Cordes
    Nancy Cordes On Twitter»

    Nancy Cordes is CBS News' congressional correspondent.