"Instead, yesterday morning just one day after the massacre he went on TV and suggested that President Obama is on the side of the terrorists," Clinton said. "Just think about that. Even in a time of divided politics, this is way beyond anything that should be said by someone running for president."
Clinton asked, "Will responsible Republican leaders stand up to their presumptive nominee?"
"Or will they stand by his accusation about our president," Clinton continued. "I'm sure they’d rather avoid that question altogether. But history will remember what we do in this moment."
As Clinton spoke, Obama delivered a denunciation of Trump that was nearly identical word for word.
He challenged Republicans to reject Trump's proposed Muslim ban, which he said makes the country less safe.
"Do Republican officials actually agree with this?" Obama asked. "Because that's not the America we want. It does not reflect our Democratic ideals."
In his speech in New Hampshire on Monday, Trump doubled down on his proposal to ban Muslims from entering the United States and expanded the prescription to all foreigners who sought to enter from Middle Eastern countries.
He accused Clinton and Obama of being incapable of responding to the threat of terrorism and falsely accused both Obama and Clinton of proposing to open U.S. borders to hundreds of thousands of unvetted refugees from the Middle East.
Clinton described Trump's response to the Orlando attacks as being rife with "conspiracy theories" and "pathological self-congratulations."
She noted that when she read through Trump's entire speech, she sifted through "bizarre rants" and "outright lies" to reveal a fixation on the words "radical Islam" and his proposed ban on Muslims.
Clinton noted that Trump said in his speech on Monday that the New York-born killer in Orlando was born in Afghanistan.
"He was born in Queens, New York, just like Donald was himself," Clinton said. "Muslim bans and immigration reform would not have stopped him. They would not have saved a single life in Orlando."
"He has to distract us from the fact that he has nothing substantive to say," Clinton added of Trump.
And earlier in the day in two television interviews, Trump repeatedly seemed to suggest that Obama might be connected to the attack or sympathized with terrorists.
"What Donald Trump is saying is hateful" and "disrespectful," Clinton said. "And it is yet more evidence that he is temperamentally unfit and totally unqualified to be president of the United States."
Clinton recalled Trump's leadership of the "birther" movement, which suggested that Obama was not born in the United States.
"So maybe we shouldn’t be surprised," Clinton said. "But it was one thing when he was a reality TV personality, raising his arms and yelling you’re fired!
"It’s another thing altogether when he is the Republican Party’s presumptive nominee for president," Clinton said.
Clinton's remarks come a day after she delivered an address focused on the threat of terrorism in Cleveland. She didn't name him, but Trump was undoubtedly the target of her message, which criticized him for proposing a ban on Muslims. Clinton called for unity and pledged that as president she would make combating "lone wolf" terrorists a top priority.
"We need leadership, common sense and concrete plans because we are facing a brutal enemy," Clinton said, referring to the Islamic State. "In the Middle East, ISIS is attempting a genocide of religious and ethnic minorities. They are slaughtering Muslims who refuse to accept their medieval ways."
Trump had long criticized Clinton and Obama for refusing to use the phrase "radical Islam" to describe terrorists.
But on Monday, Clinton sought to brush aside the controversy, calling it Trump's "fixation" with "name calling." She added that she was "happy" to use either "radical jihadism" or "radical Islamism."
Both she and Obama dismissed Trump's focus on the "magic" words "radical Islam."
Hillary Clinton on the campaign trail
"From my perspective, it matters what we do, not just what we say," Clinton said. "If Donald suggests I won't call this threat what it is, he hasn't been listening."
"But I will not demonize and declare war on an entire religion," she added. "Now that we are past the semantic debate, Donald is going to have to come up with something better."
The focus on Trump on Tuesday marks a stark departure from Clinton's more subdued comments on national security, which she delivered in Cleveland on Monday. But she returned to the themes of unity and bipartisanship, which she said should characterize American's approach to combating terrorism.
She referenced a letter from former president George H.W. Bush to her husband, former president Bill Clinton, that had been left in the Oval Office when Clinton took office in 1993. A copy of the note from Bush's presidential library had gone viral on the Internet this week.
"You will be our president when you read this note. I wish you well. I wish your family well. Your success is now our country's success and I am rooting hard for you," Bush wrote in the note.
Clinton said that rereading the note Monday brought her to tears, and her voice was heavy with emotion as she read the words aloud to her supporters.
"That's the America we love," she said.