Donald Trump doubled down on his response to the deadly attack at a gay nightclub in Florida over the weekend, telling a crowd in Atlanta on Wednesday that his administration would halt immigration from countries with a history of terrorism, and increase surveillance on U.S. mosques.

"He was born here, but his parents weren't," the presumptive Republican nominee said of Omar Mateen, the New York-born shooter who killed 49 people in Orlando, Florida, early Sunday morning. "His ideas weren't."

For months, Trump has called for a ban on Muslims entering the country. But after the Orlando attacks – and after initially claiming Mateen, a Muslim, was born in Afghanistan – Trump shifted his proposal to a country-of-origin ban, rather than one based on religion.

Instead, he reiterated a call put forward by Texas Sen. Ted Cruz, Trump's rival for the GOP nomination at the time, to increase government surveillance on Muslim places of worship.

"We have to check, respectfully, the mosques, because if we don't solve it, it's going to eat our country alive," Trump said.

He also proposed establishing safe zones inside Syria – a controversial plan that would shelter war refugees inside their country of origin – and said he wished more people inside the Pulse nightclub had been armed.

"If some of those great people that were in that club that night, had guns strapped to their waist or ankle, you would have had a different situation, folks," he said.

Trump hammered President Barack Obama and presumptive Democratic nominee Hillary Clinton for refusing to say the term "radical Islamic" terrorism.

"Unless you're willing to [say the] name of the problem...you're never going to solve the problem," he said.

Clinton and Obama, who favor the term "radical Islamism" instead, say it better reflects how violent, militant groups like the Islamic State have perverted a peaceful religion. Saying "radical Islam," they argue, unfairly sweeps in the faith's 1.6 billion worldwide practitioners and alienates potential allies in Muslim-majority countries best positioned to fight extremism at its source.

"He has been fixated on the phrase radical Islam as if those are magic words that would stop terrorists," Hillary Clinton said during a national security address in Virginia around the same time Trump held the Atlanta rally. "His approach isn't just wrong, it is dangerous."

"Not one of Donald Trump's reckless ideas would have saved a single life in Orlando," she said.

Clinton and Trump, however, may soon find themselves in agreement on one proposal.

Trump said Wednesday he plans to meet with the National Rifle Association over legislation favored by Democrats and a handful of Republicans in Congress that would prohibit anyone on a federal terror watch list from buying a gun.

