Donald Trump in particular devoted large parts of the debate to interrupting Joe Biden and moderator Chris Wallace.
Joe Biden also received several reprimands for the same thing during the debate, which was seen by millions of Americans.
The organizer, the Commission for Presidential Debates, now writes in a statement that: "Last night's debate made it clear that more structure needs to be added to create a more orderly discussion of the issues".
The new "structures" have not yet been announced but will, according to the statement, "be adopted and announced shortly".
Many viewers have, among other things, asked for opportunities to turn off candidates' microphones, or time deductions for those who interrupt the other candidate, but the question of the form of the debates is also a sensitive one.
Both parties have agreed in advance jointly on the current forms of the debates.
In theory, there is thus a risk that the parties will say no to the proposed changes, and then the question is whether there will be more debates.
Since 1988, the Commission has hosted presidential debates for all US presidential debates.
The impartial private organization aims to promote discussions of issues to promote the ability of the American people to be informed before the election.
After the debate, the host Chris Wallace has had to endure some criticism, but the organization expresses in its statement support for Wallace.
"The Commission would like to express its gratitude to Chris Wallace for the professionalism and skill he demonstrated during the debate, and we intend to ensure that additional tools for creating order are in place for the remaining debates."
The next debate will take place on October 7 between Vice Presidential candidates Mike Pence and Kamala Harris.
This is followed by two further debates with Trump and Biden before the election.