Moderator Chris Wallace criticised after debate descends into chaos with constant interruptions from Donald Trump

Watch: Insults and interruptions dominate Donald Trump and Joe Biden's first debate

Fox news host Chris Wallace has come under fire for letting the first presidential debate between Donald Trump and Joe Biden descend into chaos, triggering calls for the remaining debates to be cancelled.

Mr Wallace, the sole moderator for the 90-minute debate, was heavily criticised by viewers and pundits alike for failing to keep control of proceedings after facing an onslaught of interruptions from Mr Trump.

More than halfway through the event, an agonised Mr Wallace urged Mr Trump to stop cutting into Mr Biden's time, reminding the president that his team had agreed to follow the rules of the debate, but to no avail.

Mr Trump repeatedly interrupted and pushed back on the moderator's attempts to stick to the rules and maintain order, refusing to allow Mr Biden to use his full time slot to respond to questions.

Mr Trump also turned his fire on Mr Wallace, after the presenter noted that the president had not come up with his promised health care plan in nearly four years.

"I guess I'm debating you, and not him. That's okay. I'm not surprised," Mr Trump told the moderator.

Mr Wallace hails from the president's favourite cable news network, Fox News, but is known as one of his toughest questioners at the network and has frequently faced Mr Trump's wrath.

Ahead of the debate, Mr Wallace said he wanted to be "as invisible as possible" to allow viewers to hear directly from the candidates, but appeared to have failed in his goal.

He was forced to pause proceedings at one point, telling Mr Trump: “The country would be better served if we allowed both people to speak with fewer interruptions. I’m appealing to you, sir, to do it.”

However, viewers appeared to be united in their condemnation of the night's debate.

A CBS/YouGov poll found that 69 per cent of likely voters who tuned in were left feeling "annoyed" and just 17 per cent said the exchanges left them feeling "informed".

“As somebody who has moderated presidential debates, as someone who has prepared candidates for presidential debates, as someone who has covered presidential debates: That was the worst presidential debate I have ever seen in my life,” said ABC News anchor George Stephanopoulos.

In the immediate aftermath of the shouting match, there was heated discussion over whether Mr Biden should pull out of the second and third debates.

They are scheduled to take place on October 15 and October 22, just days before election day.

Mr Wallace has previously been praised for his ability to grill Mr Trump during interviews, and his inability to rein in the president during Tuesday night's debate has not inspired confidence for the next two rounds.

"Can we really have two more of these debates, after what we saw tonight?" asked CBS presenter Nora O'Donnell. CNN's Wolf Blitzer was even more emphatic, saying: "I wouldn't be surprised if this is the last presidential debate between the president and the former vice president".

Mr Biden's communications director pushed back on the suggestion, insisting that the Democratic candidate "will be showing up for the debates".

The campaign may be concerned that walking away from the remaining debates may suggest to Americans that Mr Biden is running scared, but Democratic strategists have pointed out he has little to gain from a repeat of Tuesday night.

Watch: Trump v Biden - the seven defining moments of the US presidential debate