"You don't build a coalition by insulting our friends or acting like a loose cannon. You do it by putting in the slow, hard work of building relationships," the Democratic presidential nominee and former secretary of state said during remarks at the American Legion's national convention in Cincinnati, referring to her Republican opponent.
"Getting countries working together was my job every day as your secretary of state. It's more than a photo op. It takes consistency and reliability. Actually, it's just like building personal relationships. People have got to know that they can count on you, that you won't say one thing one day and something totally different the next.
"And," she added, "it certainly takes more than trying to make up for a year of insults and insinuations by dropping in on our neighbors for a few hours and then flying home again. That is not how it works."
Trump accepted an invitation from Mexican President Enrique Pena Nieto on Tuesday to meet today before Trump gives a speech on immigration tonight in Phoenix.
Clinton's campaign responded swiftly to news of the trip.
"What ultimately matters is what Donald Trump says to voters in Arizona, not Mexico, and whether he remains committed to the splitting up of families and deportation of millions," Clinton spokeswoman Jennifer Palmieri said in a statement Tuesday.
The campaign confirmed that Clinton, too, has received an invitation to meet with Pena Nieto. Clinton, who last met with him in 2014, has yet to accept, but her campaign says she hopes to meet with him soon.
During her speech to the American Legion, she also hit Trump for his relationship with Russian President Vladimir Putin and how Trump agreed when Putin criticized American exceptionalism.
"There's no question we face real threats and real enemies that we need to confront and defeat. My opponent is wrong when he says America is no longer great," Clinton said.
On the topic of Russia, she homed in on cybersecurity in light of recent hacks that her campaign believes were part of attempts to influence the U.S. presidential election.
"Russia has hacked into a lot of things. China has hacked into a lot of things. Russia even hacked into the Democratic National Committee," she said. "Maybe even some state election systems. So we've got to step up our game, make sure we're well defended and able to take the fight to those who go after us."
Clinton also told the veterans' organization that she will address the mental health of U.S. service members when they return home and make sure the families of fallen troops get the respect they deserve.
"I will never, ever disrespect Gold Star families who've made the ultimate sacrifice for our nation. Or prisoners of war who endured so much in our name. To insult them is just so wrong, and it says a lot about the person doing the insulting," she said, referring to Trump's attacks on the parents of slain U.S. soldier Humayun Khan after they appeared onstage at the 2016 Democratic National Convention.
Trump will address the American Legion convention Thursday.