The commission that oversees US presidential debates says it will change the format to ensure the remaining two encounters between Donald Trump and Joe Biden are more orderly.
The tone and tactics of the first presidential debate were criticised across the US and around the world.
The fallout, however, has also been dominated by Mr Trump's refusal in the debate to explicitly condemn a far-right group called the Proud Boys.
However, President Trump constantly interrupted Democratic candidate Joe Biden leading to a series of chaotic exchanges in which both men talked over each other.
The Commission on Presidential Debates (CPD) - a nonpartisan body that has organised presidential debates since 1988 - said it would soon announce new measures to help moderators "maintain order" in the remaining two debates.
During the debate, Mr Wallace asked whether the president would condemn white supremacists and tell them to stand down during protests.
When Mr Trump asked who it was he was being told to condemn, Mr Biden twice said "Proud Boys", referring to a far-right, anti-immigrant, all-male group with a history of violence against left-wing opponents.
The president said: "Proud Boys - stand back and stand by.
Mr Biden said Mr Trump had "refused to disavow white supremacists"?
Joe Biden returned to the issue in a tweet on Wednesday, saying: "There's no other way to put it: the President of the United States refused to disavow white supremacists on the debate stage last night."
In his tweet he quoted a comment, addressed to the president, from a Proud Boys online forum that read: "This makes me so happy
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