In speeches scheduled before the slayings at a gay nightclub in which 49 people and the gunman were killed, the Democratic and Republican presidential rivals discussed their starkly differing approaches to national security.
"The Orlando terrorist may be dead, but the virus that poisoned his mind remains very strong, and we must attack it," Clinton, the Democrats' presumptive nominee for the Nov. 8 election, said in a speech in Cleveland.
Trump was more critical, lashing out at President Barack Obama by questioning his motives for refusing to use the term "radical Islamic terrorism" in describing such attacks. He argued that both the president and Clinton were unfit to lead the nation.
Omar Mateen, 29, the U.S.-born son of Afghan immigrants, armed with an assault rifle and pledging loyalty to militant group Islamic State, opened fire at a gay nightclub in Orlando early on Sunday.
In proposals for dealing with threats of violence at home and abroad, Clinton called for increased efforts to remove Islamic State propaganda from the Internet, more air strikes in the areas held by the militant group and better coordination with allies in the region.
She specifically called out three U.S. allies - Saudi Arabia, Qatar and Kuwait - for allowing its citizens to fund mosques and schools that train jihadists.
She also called for stricter gun control laws, reiterating prior calls to prohibit those on terrorism watch lists from buying guns. She pointed out that while the Federal Bureau of Investigation was aware of Mateen as a possible threat, he was still able to legally purchase a gun.
Clinton has called for a complete ban on assault-style guns.
"It’s important that we stop the terrorists from getting the tools they need to carry out the attacks, and that is especially true when it comes to assault weapons like those used in Orlando and San Bernardino," California, Clinton said, drawing a standing ovation from the crowd.
Clinton called on Americans to come together in the way they did after the Sept. 11, 2001 attacks on the World Trade Center and Pentagon. She pointed out that, at the time, she was a Democratic U.S. senator representing New York, while the U.S. president, New York governor and New York City mayor were all Republicans.
"Americans from all walks of life rallied together with a sense of common purpose on Sept 12. ... We had each others' backs. We did not attack each other, we worked with each other to protect our country and rebuild our city," Clinton said. "It is time to get back to the spirit of those days, the spirit of 9/12, let's keep looking for the best within our country, the best within each of us."
TRUMP LASHES OUT AT OBAMA
Earlier, Trump questioned Obama's motives for not using the term "radical Islam" in an interview on Fox News.
"He doesn't get it or he gets it better than anybody understands," Trump said. "It's one or the other, and neither one is acceptable."
Trump has for years suggested that Obama is secretly a Muslim. In 2011, when the wealthy businessman drew national attention for demanding that Obama produce another copy of his birth certificate, he told Fox News, "maybe it says he is a Muslim." Obama is a practicing Christian.
"We're led by a man that either is not tough, not smart or he's got something else in mind," Trump said on Fox without being specific. "And the something else in mind. People can’t believe it. ... There’s something going on. It’s inconceivable."
A Trump campaign spokeswoman did not immediately respond to a request for comment.
White House spokesman Josh Earnest refused to address Trump’s comments directly, saying Trump’s remarks were “small” in the shadow of the massacre, and as such, neither he nor Obama would focus on them.
“When you are focused on something as big as helping the country respond to the worst mass shooting in our nation’s history, when you are focused on something as big as safeguarding the country and combating violent extremism, it’s important not to get distracted by things that are so small,” Earnest told reporters at the daily news briefing.
Trump on Sunday had called for Obama to resign for not using the words "radical Islam" in his comments about the shooting. He also renewed his call for a temporary ban on Muslims entering the United States.
Trump was delivering a speech on national security in New Hampshire. The topic was a change from his earlier plan to criticize Clinton.
Trump said on CNN that the United States needed better intelligence gathering to prevent incidents such as the Orlando attack.
“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 on ABC's "Good Morning America.
(Additional reporting by Susan Heavey and Alana Wise in Washington; Editing by Bill Trott and Jonathan Oatis)
