Democratic presidential nominee Hillary Clinton warned that anti-Muslim rhetoric by opponent Donald Trump is "giving aid and comfort" to Isis.
Both candidates sought to position themselves as better qualified to combat terrorism in the aftermath of a spate of violence.
"We know that a lot of the rhetoric that we've heard from Donald Trump has been seized on by terrorists, including Isis, because they are looking to make this a war against Islam," Clinton said.
She insisted that the United States is up to the challenge of combating terrorism on its shores and that only she has a detailed plan to meet that challenge.
Trump said current anti-terrorism efforts are insufficient at home and abroad. He blamed President Barack Obama and Clinton, who served as Obama's first Secretary of State, and he suggested that profiling may be necessary to counter the threat.
"We have to lead for a change. Because we're not knocking them," Trump told Fox News Channel. "We're hitting them once in a while. We're hitting them in certain places. We're being very gentle about it. We're going to have to be very tough."
A week before Clinton and Trump are scheduled to face off in their first televised debate, bombings in New York and New Jersey and a mass stabbing in Minnesota have refocused the presidential race on concerns about domestic terrorism and national security.
With the US rattled in the wake of the three attacks, both candidates made the case for why they are better prepared than the other to step into the Oval Office.
The two candidates' responses aptly reflected what each sees as a winning argument - for Clinton, an appeal to steady leadership and presidential bearing, and for Trump, a get-tough message.
At an airport news conference with her campaign plane as a backdrop, Clinton stood somberly at a lectern and repeatedly sought to encourage Americans to go about their lives, to not be deterred by fears of terrorism and to rest assured that the United States is well-positioned to address the threat at home and abroad.
In his interview, Trump said the United States is too tentative in its efforts against terrorism overseas. The better approach would be to "knock the hell out of them" and possibly introduce profiling as a counterterrorism tactic, he added.
"Our local police, they know who a lot of these people are," Trump said in the Fox interview. "They are afraid to do anything about it, because they don't want to be accused of profiling. And they don't want to be accused of all sorts of things."
He concluded: "Do we have a choice? Look what's going on. Do we really have a choice? We're trying to be so politically correct in our country."
It's not the first time Trump has suggested that profiling could be an effective tactic.
Later in the day, at the start of a campaign rally in Estero, Florida, Trump took sharp and repeated aim at Clinton, accusing her of embracing plans on immigration and refugees that are too lax. He blamed the attacks over the weekend in part on immigration laws he cast as too weak and linked them to radical Islam.
Authorities have not confirmed any connection between the suspects and terrorist groups, although a news agency linked to Isis (Islamic State) claimed that the Minnesota attacker was "a soldier of the Islamic State".
"There have been Islamic terrorist attacks in Minnesota and New York City and in New Jersey," Trump said. "These attacks and many others were made possible because of our extremely open immigration system, which fails to properly vet and screen the individuals or families coming into our country."
Trump also said the authorities should use "whatever lawful methods are available to obtain information" from the suspect. He called on Congress to pass measures ensuring foreign enemy combatants are "treated as such". Trump has in the past voiced support for bringing back waterboarding as an interrogation tactic.
Trump later added that Clinton "talks tougher about my supporters than she does about Islamic terrorists," citing her controversial statement earlier this month that half of his backers come from a "basket of deplorables". Clinton has said she regrets classifying "half" of Trump's supporters that way.
The Republican nominee also lamented that the suspected New York and New Jersey bomber - a US citizen - is likely to receive modern medical treatment and access to a lawyer.
"Now we will give him amazing hospitalisation. He will be taken care of by some of the best doctors in the world. He will be given a fully modern and updated hospital room, and he'll probably even have room service, knowing the way our country is," Trump said.
"And on top of all of that, he will be represented by an outstanding lawyer. His case will go through the various court systems for years. And in the end, people will forget and his punishment will not be what it once would have been. What a sad situation."
Trump and Clinton were scheduled to meet Egyptian President Abdel-fatah al-Sisi in New York for talks that were likely to include discussion of terrorism and prospects for peace in the Middle East.
Sisi, a former military chief who seized power in the 2013 toppling of Mohamed Morsi, Egypt's Muslim Brotherhood-backed president, is in the United States for the annual UN General Assembly.
In addition, Clinton planned to use the gathering of world leaders to hold a session with Ukraine's leader. Ukraine and Russia are at odds, and skirmishing nearly daily, over Russia's annexation of Crimea two years ago. Clinton's meeting with Petro Poroshenko, which Ukrainian officials said was at the country's invitation, is a finger in the eye of Trump and Russian President Vladimir Putin, the autocratic leader for whom Clinton has accused Trump of having a dangerous affinity. Ukraine said it also invited Trump to meet Poroshenko in New York.
Clinton, who also served as a US senator from New York, quickly pointed to her experience, in a direct contrast to that of Trump, the New York businessman who has never held elective office.
Clinton sought to reassure Americans that law enforcement and other authorities are up to the task - a clear message to voters worried about how the next administration will confront security challenges.
"This threat is real, but so is our resolve. Americans will not cower. We will prevail," Clinton said. "We will defend our country, and we will defeat the evil, twisted ideology of the terrorists."
Republicans have recently had an edge in voter trust when it comes to dealing with terrorism. But recent Washington Post-ABC News polls find that Clinton holds a three-point edge over Trump among registered voters on handling terrorism and a 24-point lead on handling an international crisis.
"I am the only candidate in this race who has been part of the hard decisions to take terrorists off the battlefield," Clinton said.
She added that she had laid out "a comprehensive plan to meet the evolving nature of this threat and take the fight to Isis everywhere they threaten us, including online."
Trump, she insisted, has no real plan.
Trump offered a vague strategy for combating Isis and other terrorists overseas.
"Maybe we're going to be seeing a big change over the last couple of days," Trump warned. "I think this is something that maybe will get, you know, will happen perhaps more and more over the country."
The emphasis on steadiness and calm, as well as experience, has been Clinton's main national-security argument in a year in which voters have sought outsider candidates and a message of change. She is constrained somewhat by the imperatives to defend Obama's foreign policy as his designated successor and not alarm liberal Democrats still suspicious of her reputation as a hawk.
In touting her credentials, Clinton pointed to the endorsements she has received from Republican national-security leaders who have voiced grave concerns about the prospect of Trump as commander in chief.