Scott Audette/REUTERS
Donald Trump.
Both candidates won several primary and caucus contests Tuesday. Clinton has long been the presumed Democratic nominee for president, and Trump is the clear Republican frontrunner.
A little after midnight EST on Wednesday, both candidates had won seven states.
Clinton won Alabama, Arkansas, Georgia, Tennessee, Texas, and Virginia. Trump won Alabama, Arkansas, Georgia, Massachusetts, Tennessee, Vermont, and Virginia, with Alaska yet to be called on the GOP side.
In their victory speeches, they each sounded as if they were already preparing for the potential faceoff in the months ahead.
"Instead of building walls, we're going to break down barriers and build ladders of opportunity and empowerment so every American can live up to his or her potential," Clinton said, in an implicit attack on Trump's calls to build a wall on the southern border of the US to combat illegal immigration.
She also took a shot at Trump's campaign slogan, "Make America Great Again."
"We know we've got work to do. It's not to make America great again," Clinton said. "America never stopped being great. We have to make America whole ... and fill in what's been hollowed out."
Trump responded with a direct attack. He charged that Clinton isn't capable of fixing America's problems.
"I watched Hillary's speech and she's talking about, 'Wages have been poor, and everything's poor, and everything's doing badly, but we're going to make it.' She's been there for so long," Trump said, referring to Clinton's long career in government.
"I mean, if she hasn't straightened it out by now, she's not going to straighten it out in the next four years. It's just going to become worse and worse," he added.
REUTERS/Scott Audette (L), Javier Galeano (R)
Donald Trump and Hillary Clinton.
Trump then responded directly to Clinton's attack on his campaign slogan.
"She wants to make America whole again, and I'm trying to figure out what is that all about," Trump said. "'Make America great again' is going to be much better than making America whole again."
Trump dinged his Republican opponents, but took particular aim at Sen. Marco Rubio and suggested he wouldn't be able to outlast Trump. He boasted about his chances against Clinton, suggesting that if he and Clinton were the presidential nominees for their respective parties, it would be an "easy race."
"Once we get all of this finished, I'm going to go after one person. That's Hillary Clinton," Trump said. "And I think that's frankly going to be an easy race. You see the polls. I beat Hillary in many polls," he added.
Republican Sen. Ted Cruz of Texas won two states on Tuesday - Oklahoma and Texas - and tried to position himself as the most viable alternative to Trump, who still doesn't have much support from the Republican establishment.
Thomson Reuters
Ted Cruz.
But at this point, it will be difficult for any Republican challenger to stop Trump, who is well on his way to the delegates he needs to snag his party's nomination. Other candidates, including Rubio, faced questions amid Trump's romp about whether he was in "denial" about a potential path to the nomination.
Bernie Sanders, the independent senator from Vermont, is still in the running for the Democratic nomination, also had a relatively strong night by winning four states. But he suffered a crushing symbolic loss in Massachusetts, which neighbors his home state of Vermont, and Clinton walked out of the night with a huge delegate lead.
Sanders argued that he could still win.
"Ten months ago, as you know ... we were at 3% in the polls. We have come a very long way in 10 months," he told supporters during an address in Vermont.
He added: "At the end of tonight, 15 states will have voted, 35 states remain. And let me assure you that we are going to take our fight for economic justice, for social justice, for environmental sanity, for world of peace, to every one of those states."