Alexander Burns and Nicholas Confessore
Before flying to Philadelphia to court younger voters, Mrs. Clinton held a news conference to call for “courage and vigilance” in the face of terrorism, and warned that Mr. Trump was unprepared to keep the country safe.
Citing former intelligence and counterterrorism officials who have criticized Mr. Trump’s caustic remarks about Islam, Mrs. Clinton leveled an attack that might have shocked the political world in any other campaign: In addition to calling him a “recruiting sergeant” for terrorists, she accused him of giving “aid and comfort” to the Islamic State with his campaign oratory.
“We’re going after the bad guys, and we’re going to get them, but we’re not going after an entire religion,” Mrs. Clinton said, adding, “We know that Donald Trump’s comments have been used online for the recruitment of terrorists.”
It was the most drastic version yet of an attack Mrs. Clinton has tried out recently with increasing boldness: In an interview on Israeli television this month, she said the Islamic State was praying for Mr. Trump’s victory, and she has warned that foreign adversaries could seek to sway the election in her opponent’s favor.
Mr. Trump, she said on Monday, has helped the Islamic State and other terrorist groups cast their attacks as part of a religious war between Islam and the West.
“They are looking to make this into a war against Islam, rather than a war against jihadists, violent terrorists,” Mrs. Clinton said. “The kinds of rhetoric and language Mr. Trump has used is giving aid and comfort to our adversaries.”
Mr. Trump responded with indignation. His campaign released a string of statements expressing outrage, criticizing Mrs. Clinton for favoring more lenient immigration policies and calling her attack on Mr. Trump tantamount to an accusation of treason.
At a rally in Florida on Monday afternoon, Mr. Trump blasted Mrs. Clinton for failing, as a member of the Obama administration, to stop the rise of the Islamic State, employing much the same throw-the-bums-out argument he has used to demand an overhaul of government on domestic matters.
“Her weakness, her ineffectiveness, caused the problem, and now she wants to be president,” he said. “I don’t think so.”
Mr. Trump directly equated American vulnerability to terrorism with what he called laxness in the immigration system. He has mainly warned about the risk of admitting refugees from Syria and other war-torn countries, though the suspect arrested in the weekend attacks, Ahmad Khan Rahami, is a naturalized citizen born in Afghanistan and has lived in the United States for years.
“These attacks, and many others, were made possible because of our extremely open immigration system,” Mr. Trump said, trying to return the political debate to the issue he is most comfortable discussing. “Immigration security,” he added, “is national security.”
But Mr. Trump may have to clear a higher standard than merely keeping up, punch for punch, with Mrs. Clinton. While he has drawn close to her in the polls, he still faces broad reservations among voters about his readiness to serve as commander in chief. In the past, he has provoked a backlash after terror attacks by fulminating against Muslims and shifting too quickly onto the offensive.
If Mr. Trump finished the day with a forceful speech denouncing Mrs. Clinton, he began with a meandering telephone interview with Fox News, during which he asserted that there were “many foreign connections” to the weekend attacks, though none had been established. And he suggested, again without supplying evidence, that American police officers fail to act against terrorism suspects because of political correctness.
Mr. Trump also applauded himself for having described the Saturday night explosion in New York City as a bombing even before the police did. “I should be a newscaster,” he said. “I called it before the news.”
The hostilities between the candidates erupted at the start of a week when both were aiming to cut a presidential profile and to strengthen their credentials on the international stage by meeting with foreign leaders in New York at the annual session of the United Nations General Assembly.
In many respects, Mrs. Clinton’s campaign against Mr. Trump has flipped the traditional contours of defense politics, offering voters a Democrat with more hawkish instincts and deeper ties to the national security establishment, and a Republican who has broadly rejected military intervention and has been spurned by many defense leaders in his own party.
Mrs. Clinton is by far the more conventionally experienced and credentialed candidate, and in some respects is more hawkish: She has called for the creation of a no-fly zone in Syria, as well as more airstrikes there, and has urged closer collaboration with Silicon Valley to expand the United States’ surveillance capabilities, alarming some civil liberties advocates.
In Mr. Trump, she confronts a candidate who has been abandoned by most of his party’s national security elite, who is still unable to produce a detailed set of proposals for stopping terrorism, and whose essential political brand — disruption — does not always comfort voters seeking strength in moments of crisis and terror.
Tommy Vietor, a former national security spokesman for Mr. Obama, said that if Democrats were conventionally cast as the “mommy party” and Republicans as the “daddy party” in American politics, then “Trump is the crazy uncle and Hillary Clinton is the only person you trust to watch your family for a week.”
Mr. Trump has also cast doubt on American participation in NATO and spoken warmly of Vladimir V. Putin, the Russian president and strongman. And in recent days, he has feuded with Robert M. Gates, a highly regarded former defense secretary, and found himself mocked by another respected national security figure, former Secretary of State Colin Powell, who called Mr. Trump “a national disgrace and an international pariah” in private emails released by hackers last week.
Whatever doubts many voters still have about Mrs. Clinton’s trustworthiness, most appear to consider her better suited to manage foreign policy and threats to the American people. Before the Chelsea bombing, according to a New York Times/CBS News poll, voters gave her a slight edge on the question of who would better handle terrorism and national security, and a large one on foreign policy. Some polling suggests that she has a bigger lead over Mr. Trump on related questions — who would be a better commander in chief, for example — than past Democratic nominees have had over Republicans.
“Voters look for the qualities of experience, temperament and judgment,” said Evan McMullin, a former intelligence officer who is running for president as a conservative independent candidate. “Hillary Clinton and Donald Trump lack some or all of them. But Trump lacks all of them.”
Correction: September 19, 2016 Because of an editing error, an earlier version of this article misstated the surname of the suspect in the bombings in New Jersey and New York. He is Ahmad Khan Rahami, not Rahmani.