The group that manages US presidential election debates said on Wednesday it would take steps to bring order to the final two contests between President Donald Trump and Democrat Joe Biden, following widespread criticism of their first encounter.

The 90-minute debate on Tuesday night was chaotic, marred by the Republican president’s constant interjections and interruptions of both his Democratic rival and the host, as well as Biden’s angry rejoinders.

The Commission on Presidential Debates, a nonpartisan group that has organised the events since 1988, said it would make unspecified changes to the format to prevent chaos.

“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 group said in a statement, adding it was “carefully considering the changes that it will adopt and will announce those measures shortly”.

Biden said in a campaign stop on Wednesday that he hoped organisers of future debates would be able to turn off the microphone of the candidate who is not speaking.

“It was a national embarrassment,” Biden said of the debate and Trump’s performance. “I am not going to speculate what happens at the second or third debate.”

The Trump campaign accused the organisation of “moving the goalposts and changing the rules in the middle of the game”.

Trump also was critical of the debate’s moderator, Fox News anchor Chris Wallace.

“Chris had a tough night,” Trump posted on Wednesday morning on Twitter, calling the debate a “two on one” fight.

The debate commission defended Wallace, thanking him “for the professionalism and skill he brought to last night’s debate” and promising “additional tools to maintain order.”

The candidates for vice president will debate next Wednesday, followed by two more presidential debates between Trump and Biden later in October.