WASHINGTON (CBSNewYork/AP) -- President Barack Obama slammed Donald Trump on Tuesday, saying the presumptive Republican nominee's anti-Muslim rhetoric is "not the America we want."
In the forceful verbal attack, the president said the U.S. was founded on freedom of religion and that there are no religious tests in America.
He also said it will make the country less safe by fueling the notion among followers of the Islamic State group that the West hates Muslims.
"If we fall into the trap of painting all Muslims with a broad brush and imply that we are at war with an entire religion, then we are doing the terrorists' work for them," he said.
Trump responded to the criticism, saying Obama puts U.S. enemies ahead of its allies and the American people.
In an emailed response to questions Tuesday, Trump said the president "claims to know our enemy, and yet he continues to prioritize our enemy over our allies, and for that matter, the American people.''
He added that "when I am president, it will always be America first.''
Obama's comments came a day after Trump doubled down on his proposal to temporarily ban foreign Muslims from entering the U.S.
On Twitter Monday, Trump said he "spoke about a temporary ban" during a recent speech, which he said includes "suspending immigration from nations tied to Islamic terror."
But the president noted Tuesday that the Orlando shooter, Omar Mateen, as well one of the suspects from the San Bernardino, California shooting and the Fort Hood shooter, were all born in America.
"Are we going to start treating all Muslim-Americans diffidently? Are we going to start subjecting them to special surveillance? Are we going to start discriminating against them because of their faith? We've heard these suggestions over the course of this campaign," he said. "Do Republican officials actually agree with this?"
The president also pushed back against criticism by Trump and others that he doesn't use the term "radical Islamic terror."
"What exactly would using this label accomplish? What exactly would it change? Would it make ISIL less committed to trying to kill Americans? Would it bring in more allies? Is there a military strategy that is served by this? The answer is none of the above," Obama said. "Calling a threat by a different name doesn't make it go away. This is a political distraction."
Obama said "there's no magic to the phrase" and said using the term is "not a strategy."
"Someone seriously thinks that we don't know who we're fighting? Is there anybody out there confused about who our enemies are?" he said. "That would come as a surprise to the thousands of terrorists we've taken off the battlefield."
In a speech to union members in Pittsburgh Tuesday, Democratic presumptive nominee Hillary Clinton asked: "Is Donald Trump suggesting that there are magic words that once uttered will stop terrorists from coming after us?''
Clinton also said Trump offered "bizarre rants'' and "demonstrative lies'' in his response to the Orlando massacre and that his comments are "way beyond anything that should be said by anyone running for president of the United States.''
She said the Republican falsely identified the native-born shooter as an immigrant, arguing that Trump's anti-immigration platform and ban on Muslims entering the country would not have "saved a single life.''
"The terrorist who carried out this attack wasn't born in Afghanistan as Donald Trump said yesterday, he was born in Queens, New York just like Donald was himself,'' she said.
Clinton also said Trump falsely accused her of wanting to allow a flood of unverified refugees into the country and eradicate the second amendment.
"We need a commander-in-chief who can grapple with our challenges in all their complexity, with real plans that actually address them,'' she says.
Clinton said Republicans should seriously consider whether they will stand by the presumptive nominee or by the (Democratic) president -- something she acknowledged would be a difficult choice.
(TM and © Copyright 2016 CBS Radio Inc. and its relevant subsidiaries. CBS RADIO and EYE Logo TM and Copyright 2016 CBS Broadcasting Inc. Used under license. All Rights Reserved. This material may not be published, broadcast, rewritten, or redistributed. The Associated Press contributed to this report.)
for more features.