Des Moines, Iowa (CNN) Donald Trump on Saturday afternoon called Hillary Clinton's use of a private email server at the State Department "a criminal problem," pouncing again on the controversy that was stirred up this weekend with a joke she made about "disappearing" messages.

"It was a terrible thing she did. It was a very foolish thing," Trump told CNN's Jeff Zeleny at the Iowa State Fair. "There was no reason to do it. She's got a big problem."

Trump's comments -- which come less than 24 hours after he suggested that the scandal will cause Clinton to drop out of the race -- follow a remark she made about Snapchat, the popular picture and video app where users' messages are automatically erased after they're seen.

"I love it," Clinton joked to a 2,100-person audience at the Iowa Democratic Wing Ding dinner in Clear Lake. "Those messages disappear all by themselves."

The joke was well received in the room, as was her fiery 20-minute speech, during which she took aim at Republicans on issues ranging from education funding to equal pay for women. The entire 2016 Republican presidential field, Clinton said, was "just like Trump without the pizzaz and the hair."

Early Saturday afternoon, Clinton's campaign doubled down, tweeting a clip of her making the joke.

"Why does Hillary love Snapchat? Watch and learn," the tweet reads.

Why does Hillary love Snapchat? Watch and learn: https://t.co/ZkevdcvZOY — Hillary Clinton (@HillaryClinton) August 15, 2015

And Clinton remained defiant when speaking to reporters at the Iowa State Fair later on Saturday afternoon, dismissing any suggestion that she was taking the controversy too lightly.

"I never sent classified material on my email and I never received any that was marked classified," Clinton said, repeating a claim she's made repeatedly. "I'm going to let whatever this inquiry is to go forward and we'll await the outcome of it."

Moreover, Clinton said, the issue isn't brought up when she meets Americans on the campaign trail.

"It is never raised in my town halls," she said.

A damaging issue

JUST WATCHED Clinton: GOP candidates are Trump without 'the hair' Replay More Videos ... MUST WATCH Clinton: GOP candidates are Trump without 'the hair' 00:58

But Clinton's joke reflects a persistent problem she's faced: On the subject of her emails, she can't get out of her own way, even as her campaign flashes public signs of nervousness about the damage the issue is inflicting.

Again, she handed Republicans a way of highlighting something that has been a major drag on her poll numbers -- with a clear majority of Americans saying that they don't view Clinton as trustworthy.

Not that her GOP opponents needed it. Speaking to reporters in New Hampshire Friday night at nearly the same time Clinton was making her speech, Trump, the front-runner in Republican presidential polls, said he doesn't see how she can survive the email issue

"There's a lot of pressure on Hillary right now. It's been brutal. It's been brutal for Hillary. And I think at some point she's perhaps not going to be able to run," Trump said. "She's going to have to end her campaign. That seems to be the thinking by so many."

Trump also speculated that Clinton's difficulties could lead to Vice President Joe Biden and former Vice President Al Gore entering the race.

Other Republicans hit Clinton over the remark. Wisconsin Gov. Scott Walker sent out a tongue-in-cheek tweet Saturday afternoon that said he had found some of Clinton's "disappearing" emails.

Tim Miller, Jeb Bush's communications director, tweeted a response to NBC's Chuck Todd, saying, "I bet she is imagining just how useful such a service would've been from 08-12!"

@chucktodd I bet she is imagining just how useful such a service would've been from 08-12! — Tim Miller (@Timodc) August 15, 2015

And America Rising, a Republican research PAC, quickly cut together a clip of Clinton making the joke on its YouTube channel.

Clinton's use of a personal email address on a private server during her four years as America's top diplomat was thrust back into the spotlight in recent days when, as a Justice Department probe into those emails expanded, Clinton's campaign turned over her server to the FBI.

On Friday, Clinton attacked Republicans who have used congressional inquiries to draw attention to the issue, vowing to not "get down in the mud with them."

But there's little doubt her email usage has hurt her campaign in the five months since news of the server's existence broke. The move to turn over the server was, in part, an acknowledgment that the issue has lessened Americans' views of Clinton's trustworthiness.

Both Clinton and Trump are in Des Moines on Saturday, where their paths could cross at the Iowa State Fair.