Former US President Donald Trump has suggested he might skip the first televised debate with his Democratic presidential rival Kamala Harris over microphone rules and his own questions about the fairness of the broadcaster.

ABC News is due to sponsor the debate, scheduled for September 10 in Pennsylvania, which is one of the key battleground states.

US media outlets say the rival camps are at odds over whether to mute the mic when the other candidate is speaking.

The Harris camp reportedly wants both candidates' microphones to be live throughout the broadcast. The Politico website says the aim is to get Trump to "lose his cool and say something impolitic."

Trump complained to reporters on Monday that the agreement was to have the microphone muted. He alleged that the other camp is trying to change the rules because Harris doesn't want a debate.

Trump also called for a different TV network to host the event. He said he wants to have a fair debate and doesn't mind facing tough questions, but that he thinks ABC News is unfair.

The debate would mark the first direct face-off between Republican Trump and Vice President Harris, who officially secured her nomination last week.