The presidential candidates, following the bombings in New York and New Jersey, sparred over who would better fight terrorism, with Hillary Clinton citing her experience as secretary of state and Donald Trump saying she had emboldened terrorists to attack the United States.
Trump, at a campaign rally in Estero, Florida, blamed poor screening of immigrants for the attacks and criticized his opponent's record.
"You can’t have vetting if you don't look at ideology," he said.
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Ahmad Rahami, a 28-year-old naturalized U.S. citizen from Afghanistan wanted for questioning in the bombings, was captured Monday after being wounded in a gun battle with police.
The arrest came just hours after police issued a bulletin and photo of Rahami.
Clinton said that she understood how to fight terrorism and that she was the only candidate who had been "part of the hard decisions to take terrorists off the battlefield."
"I have sat at that table in the Situation Room," Clinton said, adding, "I know how to do this."
The Democratic presidential nominee took questions from reporters Monday morning about the weekend bombings in Manhattan and New Jersey, which officials say increasingly look like acts of terrorism with a foreign connection.
She said Trump's comments had been "seized on by the terrorists" as a recruiting tool.
Trump, at the rally, blamed Clinton and President Barack Obama for the rise of ISIS and characterized her as weak and ineffective. He taunted Clinton for not using the term "radical Islamic terrorist."
"We will not defeat it with closed eyes or silent voices," he said. "Anyone who cannot name our enemy is not fit to lead this country."
But in June, on CNN's "New Day," Clinton did use the terms "radial jihadism" and "radical Islamism."
"From my perspective, it matters what we do more than what we say," Clinton said on "New Day." "And it mattered we got bin Laden, not what name we called him. I have clearly said we -- whether you call it radical jihadism or radical Islamism, I'm happy to say either. I think they mean the same thing."
Trump on Monday also called for the use of "whatever lawful methods are possible” to get information from Rahami before it was no longer timely.
Clinton said the attacks were "a serious challenge" that the country can meet in "concert with our values" and said she has been in favor of "tough vetting."
"Let us remember there are millions and millions of naturalized citizens from all over the world," Clinton said.
"We're not going to go after an entire religion," she added.
That was a dig at the proposals of Trump, who has said he would bar immigration from nations with ties to terrorism.
"Once again someone we were told is ok turns out to be a terrorist who wants to destroy our country & its people- how did he get thru system?" Trump wrote on Twitter.
On Facebook, he attacked Clinton, writing, "Hillary Clinton's weakness while she was Secretary of State, has emboldened terrorists all over the world to attack the U.S., even on our own soil. They are hoping and praying that Hillary Clinton becomes President - so that they can continue their savagery and murder."
Trump earlier announced that the cause of Saturday's explosion was a bomb before authorities had publicly said so.
The Republican presidential nominee told "Fox and Friends" that "I should be a newscaster because I called it before the news." He spoke in a phone interview Monday.
Trump also said he believed there was a foreign connection to the attack.
It is unclear whether Trump obtained his information from some sort of briefing. His campaign has declined to say.
Trump is also saying that people who publish bomb-making instructions in magazines and on websites should be arrested "immediately."
He said: "They're making violence possible."