In the United States, the legal action of a defendant against a plaintiff is known as a what?

In the United States, a cross-complaint is a type of Pleading that asserts a claim against any of the parties suing the person making the complaint, or against anyone else involved in the same controversy or having an interest in the same property that is the subject of the lawsuit.

The rules in many United States jurisdictions permit or require a defendant to make claims for recovery from another party using a counterclaim or a cross-claim within the answer rather than using a different kind of pleading, but some jurisdictions permit a cross-complaint to be used instead of an answer for this purpose.