Hillary Clinton vowed Monday to make stopping "lone wolf" terrorists a top priority if elected president, saying that while the shooter in the deadly weekend attacks in Orlando may be dead, "the virus that poisoned his mind remains very much alive."

In a sober national security address in Cleveland, the presumptive Democratic nominee also called for ramping up the U.S. air campaign targeting the Islamic State in Iraq and Syria. She pointedly called out U.S. partners in the region by name, saying Saudi Arabia, Kuwait and Qatar must stop their citizens from funding terrorism.

And she vigorously called for banning assault weapons, like one of the guns the Orlando shooter used.

"I believe weapons of war have no place on our streets," she said.

Clinton's address in Cleveland was supposed to mark the start of her general election campaign. But Sunday's shooting altered her plans and she avoided direct attacks on her Republican rival, Donald Trump, in her first lengthy remarks on the attacks.

Still, much of Clinton's comments were aimed at drawing policy and temperamental contrasts with Trump. The businessman has called for tougher action against terrorism, including temporarily banning Muslims from the U.S. 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," Trump said Monday on ABC's "Good Morning America."

Trump was to speak on national security later Monday in New Hampshire.

The shooting at a gay nightclub in Orlando shook the presidential race, pushing terrorism and gun violence to the forefront just as Clinton and Trump moved toward the general election.

Authorities say Omar Mateen, a 29-year-old American-born Muslim, was responsible for the shooting. FBI Director James Comey said that Mateen had "strong indications of radicalization" and was probably inspired by foreign terrorist organizations, though there was no evidence Monday that he had been directed by a network to carry out the attacks.

These apparent "lone wolf" attackers have deeply worried counterterrorism officials because they often leave fewer intelligence trails to monitor. 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, Trump redoubled his call for banning Muslims, although Mateen was an American citizen born in New York. While 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 President Barack Obama may sympathize with Islamic terrorists — a stunning statement about the current commander in chief.

"He doesn't get it or, or he gets it better than anybody understands," Trump said on Fox News Channel's "Fox and Friends." ''It's one or the other. And either one is unacceptable."

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 "radicalized," the billionaire real estate mogul said on Fox. He claimed there are Muslims living here who "know who they are" and said it was time to "turn them in."

Trump's longstanding 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 counterproductive. 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.