Hillary Clinton has vowed to conduct a national security and foreign policy that Americans could be proud of, adding that Donald Trump "just absolutely bewilders" her when he talks about his policies around the globe.
The Democratic presidential candidate embraced the US Olympic team's success at a voter registration rally in Philadelphia, describing it as an example of an optimistic nation that runs counter to what she considers Mr Trump's pessimism and negativity.
"It just absolutely bewilders me when I hear Donald Trump try to talk about national security," Mrs Clinton said, pointing to US vice president Joe Biden's dissection of Mr Trump's foreign policy at a Pennsylvania event on Monday.
"What (Trump) often says hurts us. It sends the wrong message to friend and foe alike."
Referring to the Olympic team, she said: "Team USA is showing the world what this country stands for."
Mr Trump said on Monday that the country's national security requirements demanded "extreme" vetting of immigrants seeking admission to the United States, pointing to the threat of the Islamic State group (IS) and terrorism elements.
However, he offered few specifics about how the process might work or how it would be paid for by taxpayers.
Mrs Clinton and Mr Trump have each sought the upper hand as the chief executive most capable of battling terrorism.
While the GOP business mogul has vowed to project strength and decisive action against terror, the former secretary of state has pointed to her deep foreign policy credentials and warned that Mr Trump could plunge the nation into another war.
It’s not just that Trump doesn’t know what he’s talking about when it comes to national security. His words are dangerous, and they hurt us.— Hillary Clinton (@HillaryClinton) August 16, 2016
Mr Trump has previously called for an unprecedented temporary ban on Muslims entering the US, and said in his Ohio speech that he would overhaul the nation's screening process and block those who sympathise with extremist groups or fail to embrace American values.
The Republican nominee has made changes to the nation's immigration system and the construction of a wall along the Mexican border a key part of his fight against terrorism and IS, which he compared to the struggle against communism during the Cold War.
As president, Mr Trump said, he would encourage immigrants to assimilate and urge parents, teachers and others to promote "American culture".
However, he declined to say which regions of the world would face "extreme" vetting and how federal agencies would go about conducting the review.
On Tuesday, Mr Trump was travelling to Milwaukee, the site of ongoing protests over the fatal shooting of a black man by a black police officer.
His visit follows several days of violence that has left businesses in flames and the Milwaukee police chief expressing surprise at the level of unrest.
Mrs Clinton said during a stop in Scranton, Pennsylvania, on Monday that the Milwaukee protests showed the nation had "urgent work to do to rebuild trust between police and communities" and that "everyone should have respect for the law and be respected by the law".
Donald Trump says he'll create a new test for immigrants.
It's a test he'd fail.https://t.co/LZoCq8bJFx— Hillary Clinton (@HillaryClinton) August 16, 2016
In an interview on Fox News Channel, Wisconsin Governor Scott Walker accused Mrs Clinton of "inflaming the situation" with her comments.
"I think people understand in that neighbourhood and Sherman Park and in Milwaukee, they want law enforcement to step up and protect them," he said, adding that "statements like that" from Mrs Clinton and a "lack of leadership" from President Barack Obama "only inflame the situation".
Mr Trump was expected to hold an event with veterans and law enforcement officers on Tuesday.
While polls have shown Mrs Clinton building a lead following the Philadelphia convention, Democrats are fearful that a depressed voter turnout might diminish support among the minority, young and female voters who powered Mr Obama to two victories.
Mrs Clinton said at the voter registration event at a Philadelphia high school that she is "not taking anybody anywhere for granted" in the race for the White House, saying the stakes "could not be higher".
While guarding against complacency, Mrs Clinton is also preparing for a potential administration.
Her campaign announced that former interior secretary Ken Salazar, a former Colorado senator, would chair her White House transition team.
It will also include former national security adviser Tom Donilon, former Michigan governor Jennifer Granholm and two long-time Clinton advisers: Neera Tanden, the president of the Centre for American Progress, and Maggie Williams, who now leads the Institute of Politics at Harvard University.
Her team, which is being overseen by campaign chairman John Podesta, will handle long-term planning for a potential Clinton White House should the former secretary of state win the election in November.
Mr Trump has already tapped New Jersey Governor Chris Christie to lead his transition efforts.
By law, both nominees have access to national security and other federal government briefings.