Republican U.S. President Donald Trump and his Democratic challenger, former Vice President Joe Biden, are heading back on the campaign trail Wednesday, a day after they ridiculed each other with taunts and insults in a debate described by election pundits as the worst ever in modern American political history.

Trump is headed to Minnesota, a Midwestern battleground state that he narrowly lost in 2016 but hopes to recapture against Biden. Polls show the president trailing in the state and throughout the country five weeks ahead of the November 3 election.

Trump is attending a campaign fundraising event at a private home near Minneapolis, the state's biggest city, then heads to Duluth, the westernmost Great Lakes shipping port in the U.S., for a rally with supporters.

Biden started a campaign train trip through parts of Pennsylvania and Ohio, two political battleground states that Trump won four years ago against Democrat Hillary Clinton but where polls show Biden has pulled ahead of the president.

Biden is especially attempting to recapture blue collar workers in the two states that historically have voted for Democrats but turned to Trump in 2016.

After pillorying each other in Tuesday's debate as unfit to lead the country for the next four years, the two candidates resumed their attacks Wednesday on Twitter.

Trump claimed, "Nobody wants Sleepy Joe as a leader, including the Radical Left (which he lost last night!)." The president said Biden "disrespected" Bernie Sanders by "effectively calling him a loser!" Sanders, the Vermont senator who is the leader of the Democrats' progressive wing, was the last remaining Democratic contender opposing Biden for the party's presidential nomination before conceding the race to him earlier this year.

Biden offered his assessment of the debate, saying, "You heard a lot come out of President Trump's mouth. Can you name one thing he said to actually make your life better?"

In a video, the Biden campaign attacked Trump for declining during the debate to reject the support of white supremacists.

"There's no other way to put it: The president of the United States refused to disavow white supremacists on the debate stage last night," the Biden campaign said.

The video showed a snapshot of Trump saying "Stand back and stand by" when referring to the Proud Boys, a far-right, fascist group.

White supremacist groups seemingly rejoiced on social media in reaction to Trump's debate stage remark, tweeting in response, "Standing by sir."

Both Trump and Biden campaign officials were predictably pleased with their candidate's debate performance, but political analysts deplored the rancor and the fact that Trump and Biden often interrupted each other and talked over each other, with Trump the main offender.

More than an hour into the debate, moderator Chris Wallace, a Fox News journalist, rebuked the president for not adhering to the debate rules agreed to ahead of time by the two campaigns that each candidate would allow the other to finish answering questions unimpeded.

Trump and Biden are set to debate each other twice more in the coming weeks, on October 15 and 22, after next week's debate between their respective vice-presidential running mates, Vice President Mike Pence and California Senator Kamala Harris.

It is not immediately clear what could prevent another verbal free-for-all encounter between Trump and Biden, short of moderators cutting off the microphones to let Trump and Biden answer questions without the other interrupting.

University of Virginia political analyst Larry Sabato posted a blunt message on his Twitter account: "CANCEL THE REMAINING PRESIDENTIAL DEBATES."

No matter which candidate might have gained any political advantage from their Tuesday night encounter, key journalists said any undecided voters looking to gain insight into the campaign were disadvantaged.

NBC television anchor Lester Holt called it "a low point in political discourse."

Veteran Washington Post political analyst Dan Balz said, "Judging the debate by traditional standards gives the evening more credit than it deserves. For most people, this was unwatchable, a grab-the-remote, change-the-channel moment in a forum that in past election years has served the country well. What two more debates like this will accomplish is hard to imagine, other than to heighten tensions in a country already on edge."

Markus Feldenkirchen of the German newsmagazine Der Spiegel posted on Twitter, saying, "The debate was a joke, a low point, a shame for the country. Roaring, insults, two over-70s who interrupt each other like 5-year-olds - and a moderator who loses all control. The trigger, of course: Trump's uncouth, undignified behavior."