The Fox News anchor had said ahead of the event that he would try to be “as invisible as possible” during proceedings. But he was forced to repeatedly challenge Mr Trump to abide by the debate rules his campaign agreed to.
“Mr President, I am the moderator of this debate, and I would like you to let me ask my question and then you can answer it,” he told the president, following repeated interruptions of Mr Biden’s answers.
In another testy exchange, he said: "You know, sir, if you wanna switch seats, we could do that."
Despite his best efforts, Mr Wallace received criticism from debate-watchers, who suggested he did not do enough to prevent the interruptions.
Brian Stelter, CNN’s chief media correspondent and author of ‘Hoax’, a book about Fox News, said that in reference to that comment: “Yes, but the metaphorical switch happened in the first 5 minutes. Trump took control by interrupting and interjecting while Joe Biden spoke.”
He added: “Wallace belatedly tried to exert control, but rarely if ever succeeded. So Trump basically moderated tonight's debate – and Biden took full advantage of his behavior and used it as an argument to end Trump's presidency.”
Documentary filmmaker Michael Moore posed the question: “Does Chris Wallace know who Trump is? Has he seen the past four years? Wallace needs to excuse himself (his voice is shaking) and leave the stage. Is there a back up moderator in the wings? Any female journalist will do.”
Walter Shaub, former director of the US office of government ethics, said Mr Wallace “was a disaster.”
Adam Serwer, a staff writer at The Atlantic, said Mr Wallace “gave Trump the opportunity to undermine the integrity of the election.”
Democratic strategist Tom Watson said: “The worst debate moderator in the history of the United States is named Chris Wallace. That's permanent.”