The Commission on Presidential Debates on Wednesday said the highly contentious first debate between President Trump and Joe Biden “made clear” that “additional structure” should be added to the format of the remaining debates in order to “ensure” a “more orderly discussion” of issues.

The commission’s comments came after Tuesday night’s debate in Cleveland, Ohio, included repeated interruptions and both candidates hurling charges and insults at each other.

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“The Commission on Presidential Debates sponsors televised debates for the benefit of the American electorate,” the CPD said in a statement Wednesday. “Last night’s debate made clear that additional structure should be added to the format of the remaining debates to ensure a more orderly discussion of the issues.”

The commission added that it will be “carefully considering the changes that it will adopt and will announce those measures shortly.”

“The commission is grateful to Chris Wallace for the professionalism and skill he brought to last night’s debate and intends to ensure that additional tools to maintain order are in place for the remaining debates,” the commission said of the Fox News anchor, who moderated the debate.

Both candidates interrupted each other frequently. According to a Fox News analysis, Biden interrupted Trump 49 times and Wallace 18 times for a total of 67 times. Trump, meanwhile, interrupted Biden 71 times, Wallace 74 times for a total of 145 times, according to the analysis.

The CPD is sponsoring two more debates for Trump and Biden, one on Oct. 15 in Miami, Fla., and one on Oct. 22 in Nashville, Tenn. A vice presidential debate is set for Oct. 7.

“They’re only doing this because their guy got pummeled last night," Trump campaign Communications Director Tim Murtaugh told Fox News. "President Trump was the dominant force and now Joe Biden is trying to work the refs. They shouldn’t be moving the goalposts and changing the rules in the middle of the game.”

The debate got personal right out the gate Tuesday night with the former vice president calling Trump "the worst president America has ever had" and Trump saying that there is "nothing smart" about Biden.

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Leading up to the debate, sources close to the Biden campaign told Fox News that the former vice president wouldn’t engage in personal attacks or respond to any insults leveled against him by Trump.

But Biden, within the first half of the debate, slammed the president as a “liar” and a “clown” and repeatedly called on him to “shut up.”

“Would you shut up, man?” Biden said to Trump, calling him “unpresidential.”

Later, Biden cut Trump off again, saying: “Will he just shush for a minute?”

Meanwhile, the president slammed Biden, saying the former vice president is not “smart.”

“Don’t ever use the word smart with me,” Trump said. “Nothing smart about you Joe.”

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The president, when asked about his campaign rallies, said that Biden doesn’t hold events because “nobody shows up to his events.”

“People want to hear what I have to say,” Trump said.

The debate shifted to taxes. Biden vowed to repeal the "Trump tax code," and the president cut him off questioning why he didn't propose a better tax plan during his "47 years" in Washington.

"Because you weren’t president screwing things up," Biden said. "You're the worst president America has ever had.”

Fox News' John Roberts and Paul Steinhauser contributed to this report.