MOUNT PLEASANT, Iowa - President Donald Trump and Democrat Joe Biden spent Tuesday trading insults — sometimes almost simultaneously— as they stumped across Iowa in split-screen moments that could preview a ferocious fight ahead if the two face off for the presidency next year.

Biden's name recognition and a sense among some Democrats that he could beat Trump has helped him climb to the top of his party's crowded presidential field. But Trump said Biden only gained in the polls because he went on the offensive against the president himself, and he linked the former vice president to 2016 foe Hillary Clinton.

"People don't respect him," Trump said after touring a renewable energy facility in Council Bluffs. " Even the people that he's running against, they're saying: 'Where is he? What happened?'"

With a dose of exaggeration, the president added: "He makes his stance in Iowa once every two weeks and then he mentions my name 74 times in one speech. I don't know. That reminds me of Crooked Hillary. She did the same thing."

At almost the same moment in Mount Pleasant, Biden noted the attention he has been getting from Trump. Biden's appearances from earlier in the day were playing on TV screens when Air Force One landed in Iowa.

"I guess he's really fascinated by me," said Biden, who mentioned Trump by name about a dozen times during his first two events in Iowa. " I find it fascinating." He started to say more but then stopped himself, quipping: "My mother would say: 'Joey, focus. Don't descend. Stay up.'"

Pressed later by reporters about his repeated assurances that he wouldn't openly criticize Trump while campaigning, Biden said, "By not talking about him personally — talking about where I disagree with him on the issues, why he's doing such damage to the country — that's totally different than attacking his character or lack thereof."

Speaking Tuesday night in Davenport, Biden said voters must stop the president's attempts to elevate his office beyond its traditional limits of power. Trump is "breaking down the barriers that constrain his power," Biden said, and acting like he has "complete power."

"No, you don't, Donald Trump!" Biden thundered into the microphone, sparking cheers from a crowd of around 500 at the Mississippi Valley Fairgrounds.

The back and forth between Trump and Biden laid bare the rising political stakes for each man, even with the election about 17 months away.

Trump has zeroed in on Biden as a potential threat to his reelection chances and is testing themes to beat him back. Biden, meanwhile, is campaigning as a front-runner, relishing the one-on-one fight with Trump while making sure he doesn't ignore the demands of the Democratic primary.

AP