The speaker has previously hinted at the potential for an impeachment inquiry into Mr Biden.
“The public knows who I am & what a successful Presidency I had…I WILL THEREFORE NOT BE DOING THE DEBATES!” Mr Trump wrote.
France’s President Emmanuel Macron pulled through a no-confidence vote on Monday.
Mr McCarthy is set to start as speaker in January when the new Congress is sworn in.
If the Democrats lose their majority in Congress, Republicans are likely to block the majority of Mr Biden’s policies.
Michelle Obama was the most admired woman in 2020, Gallup found.
