Hillary Clinton accused Donald J. Trump on Monday of imperiling American national security with his campaign rhetoric, as Mr. Trump called for police profiling of people from the Muslim world in the aftermath of bombings in New York and New Jersey.
Just around the time the police were closing in on a suspect, Ahmad Khan Rahami — who was later taken into custody — Mrs. Clinton and Mr. Trump were split in their reactions to the attack in Manhattan on Saturday, which injured dozens. Both shifted into the mode of combat, with Mrs. Clinton stressing her national security credentials and measuring her words, and Mr. Trump sounding a note of furious alarm.
But the stakes for both candidates are likely higher now than they have ever been. With seven weeks left until the election and only a week before their first debate, their handling of a potential terrorism plot on American soil could leave a durable imprint on undecided voters.
Mrs. Clinton moved to take control of the debate with a cutting attack on Mr. Trump on Monday: At a morning news conference inside an airport hangar in rainy Westchester, she urged Americans to show “courage and vigilance,” and not to demonize Muslims or Americans of foreign origin.
And describing herself as the only candidate in the race with experience fighting terrorism, Mrs. Clinton charged that Mr. Trump had helped the Islamic State and other terror groups with his campaign oratory broadly denouncing Muslims.
Citing former intelligence and counterterrorism officials who have criticized Mr. Trump, Mrs. Clinton branded the Republican nominee as a “recruiting sergeant for the terrorists.”
That criticism is 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, Mrs. Clinton said the Islamic State was praying for Mr. Trump’s victory, and she has warned donors at private events that foreign adversaries could seek to sway the election in her opponent’s favor.
Mr. Trump, she said on Monday, had helped the Islamic State and others 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, adding, “The kinds of rhetoric and language Mr. Trump has used is giving aid and comfort to our adversaries.”
The Trump campaign responded with expressions of outrage. Jason Miller, a spokesman for Mr. Trump, said in a statement that Mrs. Clinton was effectively “accusing Mr. Trump of treason.” And ahead of a campaign rally in Florida on Monday afternoon, Mr. Trump blamed Mrs. Clinton in a Facebook post for having “emboldened terrorists” as secretary of state.
“They are hoping and praying that Hillary Clinton becomes president – so that they can continue their savagery and murder,” Mr. Trump wrote, in an almost precise echo of Mrs. Clinton’s recent rebukes of him.
The eruption of hostilities between the candidates came at the start of a week when both were aiming to cut a presidential profile, and to bolster their credentials on the international stage by meeting with foreign dignitaries in New York for the annual meeting of the United Nations General Assembly.
Mrs. Clinton was scheduled to confer with a series of foreign leaders, including Prime Minister Shinzo Abe of Japan and President Petro Poroshenko of Ukraine, and both she and Mr. Trump announced plans to meet with President Abdel Fattah el-Sisi of Egypt.
But the weekend attacks and Monday’s manhunt cast the candidates’ jousting over national security in a grimmer and more urgent context.
Mr. Trump, who has previously faced a backlash for his heated spoken and written words after terror attacks, also vented unfiltered fury over the blasts in New York and New Jersey. Having reacted to past attacks by calling for a crackdown on Muslim immigration and on Muslim communities in the United States, Mr. Trump again recommended more aggressive policing to thwart future plots.
In a telephone interview with Fox News that lasted most of a half-hour, Mr. Trump sketched a dark picture of the country as being under siege from international terrorists, and handcuffed in its ability to respond.
He asserted that law enforcement was being held back from intervening against suspected terrorists because of sensitivities about racial profiling. Mr. Trump also declared that there were “foreign connections” behind the attacks. He offered no evidence for either assertion.
“There’s many foreign connections,” Mr. Trump said. “I think this is one group. O.K., this is one group. But you have many, many groups, because we’re allowing these people to come into our country and destroy our country.”
Because of political correctness, Mr. Trump said, the police shy away from stopping even somebody who “looks like he’s got a massive bomb on his back.”
“If he looks like he comes from that part of the world, we’re not allowed to profile,” Mr. Trump said.
He also said that people who disseminate information about bomb-making in magazines should be prosecuted for inciting violence. And his campaign released a statement accusing the Obama administration of “minimizing the ISIS threat.”
In some respects, the clash on Monday encapsulated the larger contrast in the race between Mr. Trump and Mrs. Clinton, and the differences in policy and political strategy that are likely to define the remainder of the campaign.
Mrs. Clinton plainly believes that she must present herself as an authoritative but steady hand in moments of violence, rather than trying to match Mr. Trump in the volume and intensity of his remarks. She has generally led Mr. Trump in most polls, though narrowly, asking voters which candidate they trust more on matters of national security and foreign policy.
Mrs. Clinton emphasized her experience in government on Monday, saying repeatedly that she had been involved the fight against terrorism in the past. “I’m the only candidate in this race who’s been part of the hard decisions to take terrorists off the battlefield,” she said.
She did not reiterate the finer points of her plan to attack the Islamic State and its sympathizers, some of which might have the effect of distancing her from the Obama administration or irritating the left. Mrs. Clinton has called for increased surveillance, especially online, and for the creation of a no-fly zone in Syria and increased airstrikes there.
Mr. Trump, having campaigned as a fiery nationalist throughout the 2016 campaign, has continued to channel the anger and fear of voters alarmed by terrorism. And while polls show voters have doubts about Mr. Trump’s temperament and judgment, they have also regularly named him as the candidate they trust more to handle the Islamic State.
Still, Mr. Trump, who drew criticism over the weekend for having declared that a bomb went off in New York, before the police had confirmed that fact, was unabashed about his lack of restraint on Monday. On Fox, Mr. Trump applauded himself for having been proven right about the blast.
“I should be a newscaster,” he said. “I called it before the news.”