Hillary Clinton has vowed to make stopping "lone wolf" terrorists a top priority if elected president.
The Democratic presumptive nominee said that while the gunman in the deadly shootings in Orlando may be dead, "the virus that poisoned his mind remains very much alive".
In a sober national security address in Cleveland, Mrs Clinton also called for ramping up the US air campaign targeting Islamic State in Iraq and Syria.
She pointedly called out US partners in the region by name, saying Saudi Arabia, Kuwait and Qatar must stop their citizens from funding terrorism.
And she vigorously reiterated her call for banning assault weapons, like one of the guns the Orlando attacker used.
"I believe weapons of war have no place on our streets," she said.
Mrs Clinton's address in Cleveland was supposed to mark the official start of her general election campaign against Republican Donald Trump. But Sunday's shooting altered her plans and she avoided direct attacks on her Republican rival, declaring "Today is not a day for politics".
Still, much of Mrs Clinton's comments were aimed at drawing policy and temperamental contrasts with Mr Trump. The businessman's initial responses to the Orlando attacks included accepting "congrats" for "being right" about the terror threat facing the US.
He also redoubled his calls for temporarily banning Muslims from the US and increasing surveillance of mosques - policies that have concerned even some of his fellow Republicans.
"We have to have a ban on people coming in from Syria and different parts of the world with this philosophy that is so hateful and so horrible," Mr Trump said.
Because the gunman was American-born and lived in Florida, Mr Trump's ban would not have prevented the shooting.
The presumptive Republican nominee was to speak on national security later on Monday in New Hampshire. He had planned to use the speech to make his case against Mrs Clinton, as well as her husband Bill Clinton, but he, too, changed his focused after the shooting.
Authorities say Omar Mateen, a 29-year-old American-born Muslim, was responsible for the horrific attacks. FBI director James Comey said Mateen had "strong indications of radicalisation" and was probably inspired by foreign terrorist organisations, though there was no evidence that he had been directed by a network to carry out the attacks.
These apparent "lone wolf" attackers have deeply worried counter-terrorism officials because they often leave fewer intelligence trails to monitor.
Mrs Clinton said she would put together teams of government and private sector officials to try to identify lone wolf terrorists and ensure law enforcement agencies have the resources they need for such efforts.
In his morning television interviews, Mr Trump redoubled his call for banning Muslims, although Mateen was an American citizen born in New York. While Mr Trump focused in particular on keeping out refugees from Syria, he said a ban should apply to people from "different parts of the world with this philosophy that is so hateful and so horrible".
The presumptive Republican nominee also appeared to suggest that US President Barack Obama may sympathise with Islamic terrorists.
"He doesn't get it or, or he gets it better than anybody understands," Mr Trump said. ''It's one or the other. And either one is unacceptable."
Mr Trump said there were thousands of people living in the United States "sick with hate" and capable of carrying out the same sort of massacre.
"The problem is we have thousands of people right now in our country. You have people that were born in this country" who are susceptible to becoming "radicalised", the billionaire said. He claimed there are Muslims living here who "know who they are" and said it was time to "turn them in".
Mr Trump's long-standing proposal to temporarily ban foreign-born Muslims from entering the United States has triggered outrage from Democrats and Republicans alike, who see it unconstitutional, un-American and counter-productive.
But it has helped him win over many primary voters who fear the rise of Islamic extremism and believe that "political correctness" - the fear of offending Muslims - is damaging national security.