The presidential candidates threw attacks at each other on Tuesday evening in Ohio. Joe Biden asked Donald Trump to “shut up” after the president interrupted him numerous times.
On Wednesday, the US presidential commission said the first 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”.
One option on the table would be to give the moderator the ability to cut off a candidate’s microphone while the other participant is talking, a source told AP.
The next debate between the two White House hopefuls is set to take place on 15 October in Miami.
The Nielsen company announced that 73.1 million people watched the debate on television on 16 different networks.
That is more viewers than any other TV event in the US since the Super Bowl.
But it did not quite reach President Trump and Hillary Clinton’s debates in 2016 which hit 84 million viewers.
The moderator, Fox News host Chris Wallace, struggled to keep control of the debate which features several interruptions, primarily from Mr Trump.
The candidates interrupted Mr Wallace or their opponent 90 times during the 90-minute-long debate.
Mr Trump replied: “Ask him, too.”
But Mr Wallace said to the president: “Well, frankly, you’ve been doing more interrupting than he has.”
On Wednesday, Mr Biden called the debate “a national embarrassment”.
Mr Trump’s campaign communications director, Tim Murtaugh, said the commission were “only doing this because their guy got pummelled last night.
President Trump was the dominant force and now Joe Biden is trying to work the refs.”
ABC News’ Martha Raddatz, who moderated one of Mr Trump and Hillary Clinton’s presidential election debates, said Mr Wallace was placed in a nearly impossible situation.
Ms Raddatz said she never technically had the option to cut off a candidate’s microphone when she moderated.
Muting candidates is also not in the rules that Mr Trump and Mr Biden agreed with the commission in advance.
Ms Raddatz added: “To say, ‘He’s not going to follow the rules so we aren’t, either,’ It’s an unprecedented situation.
“That was so out of control.”