Fox News anchor and the host of the first US presidential debate Chris Wallace has defended his handling of the debate following criticism over his hosting. 

The "Fox News Sunday" anchor moderated the first of three debates between President Donald Trump and former Vice President Joe Biden. The 72-year-old was criticised for the chaotic nature of the debate that was marred by frequent interruptions, forcing Wallace to remind the candidates that they had agreed not to speak over each other in the debate rules.

At one point, Wallace told Trump: "Mr. President, you're not the moderator” and frequently called for calm. 

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In his first interview since Tuesday's debate, Wallace told the New York Times that he "never dreamt that it would go off the tracks the way it did."

“Generally speaking, I did as well as I could, so I don’t have any second thoughts there,” Wallace said. "I’m just disappointed with the results. For me, but much more importantly, I’m disappointed for the country, because it could have been a much more useful evening than it turned out to be."

Wallace, who moderated the final 2016 presidential debate between Trump and Hillary Clinton, added: "I’m a pro. I’ve never been through anything like this."

Wallace said he agreed with his critics, admitting, "I don’t know that I ever really did" seize control of the debate. He added however that he didn't have "advance warning" of Trump’s game plan.

"I’ve read some of the reviews, I know people think, Well, gee, I didn’t jump in soon enough. 

"I guess I didn’t realize – and there was no way you could – that this was going to be the president’s strategy, not just for the beginning of the debate but the entire debate.”

During the debate, Wallace told the candidates, "I think that the country would be better served if we allowed both people to speak with fewer interruption." Directly to Trump, Wallace added, "I'm appealing to you sir to do that." 

Wallace told the Times that he felt "desperation" at that exact moment. 

"As somebody who has said from the very beginning that I wanted to be as invisible as possible… (You’re reluctant) to rise to the point at which you begin to interject more and more," 

He added. "First to say, 'Please don’t interrupt,' then 'Please obey the rules,' and third, 'This isn’t serving the country well.' Those are all tough steps at real time, at that moment, on that stage."

Many called for microphones to be cut or for a tougher stance during questions however, the Commission on Presidential Debates said that "additional structure should be added to the format of the remaining debates."

Defending the decision not to mute mics, Wallace said: "Even if the president’s microphone had been shut, he still could have continued to interrupt, and it might well have been picked up on Biden’s microphone," he said. "It still would have disrupted the proceedings in the hall."

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Though the commission thanked Wallace for his "professionalism and skill," Wallace admitted that he doesn't "feel much like celebrating."

"I'm just sad with the way last night turned out," 

The next scheduled debate between Trump and Biden is a town-meeting format to be held on October 15 in Miami that will be moderated by C-SPAN political editor Steve Scully.

Offering some advice for Scully, Wallace warned: "If either man goes down this road, I hope you’ll be quicker to realize what’s going on than I was."

The US presidential debate commission says it will make changes to future debate formats to avoid a repeat of the disjointed first meeting between Donald Trump and Joe Biden.

Moderator Chris Wallace struggled to keep control of the debate because of frequent interruptions, primarily by the president.