The Trump campaign denies the presumptive GOP nominee was implying that he was connecting President Obama in any way to the Orlando attacks in television interviews he conducted Monday. But he continues to question the president's commitment to fighting terror.

"President Obama claims to know our enemy, and yet he continues to prioritize our enemy over our allies, and for that matter, the American people," Trump said in a statement. "When I am President, it will always be America First."

Obama spent part of Tuesday denouncing Trump's plan to bar Muslims from entering the country.

"Do Republican officials actually agree with this?" Obama said on Tuesday. "Because that's not the America we want."

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In response, Trump said at a North Carolina rally Tuesday evening that Obama was "more angry at me" than at the gunman responsible for killing 49 in the Orlando massacre.

Trump's most recent comments Tuesday echoed a foreign policy speech he delivered Monday in New Hampshire, in which the candidate forcefully defended his temporary Muslim ban plan and even said he could enact it unilaterally.

In a series of interviews throughout the day on Monday, Trump seemed to imply to various hosts that the president had ulterior motives in the Oval Office regarding Islamic terrorism. On Fox, Trump said, "He doesn't get it or he gets it better than anyone understands. It's one or the other, and either one is unacceptable."

When asked about those comments on Howie Carr's radio show on WRKO, Trump said, "Well, you know, I'll let people figure it out for themselves, Howie, because to be honest with you, there certainly doesn't seem to be a lot of anger or passion...when we want to demand retribution for what happened over the weekend."

Trump also told Carr that a president has a right to ban Muslims from the country.

"The president has the right to ban any group or anybody....that he feels is going to do harm to our country," Trump said. "They have an absolute right, Howie. And so the president of the country has the right to do this. Everyone was saying and you've heard it for a long time that - that right didn't exist. But it does exist. And everybody knows that and I thought I should point it out officially."

The controversial comments didn't stop there. He told conservative commentator Sean Hannity on his radio show that large amounts of Syrians were coming in through the southern border, making a wall there even more necessary, and that most Afghan immigrants supported Sharia law.

A large number of top Republicans also denounced Trump's comments from yesterday.

In a press conference, House Speaker Paul Ryan said he disagreed with Trump's plan to ban Muslims.

"I disagree with him because obviously, I stand by what I said," Ryan said. "We are at war with radical Islamic terrorism. And yes there is a very important distinction that needs to be made from the millions of moderate Muslims who are our allies, our brothers and sisters, who are helping us in this fight. But that does not mean we should ignore the threat that is facing us. We need to call this threat for what it is if we are to fully confront it."

South Carolina Sen. Lindsey Graham, a frequent Trump critic, said, "This idea of shutting America off to everybody in the Muslim faith makes it harder to win the war, not easier."

Even a supporter, Tennessee Senator Bob Corker, admitted that he was "discouraged" by Trump's response to the Orlando attacks.

For his part, Trump doesn't seem to be paying any heed to the avalanche of criticism that has come his way. In a separate interview with Sean Hannity, this time for television and airing on Tuesday night, Trump said that he "shamed" presumptive Democratic nominee Hillary Clinton into saying radical Islam and that he was much better for the gay community than her.

"Yes, she was shamed into it by me, and that's because of the pressure I put on her," Trump said.

"Here's a woman that takes all of this money from all of these countries, and then she says that she loves women and she's totally with the gays and, you know, whatever group you might talk about; the gays and lesbians. Now, let me just say, Sean, how can she be? They want to kill - they throw them off buildings. They actually throw gays off buildings."