(a) When defendant may bring in third party. At any time after commencement of the action a defendant, as a third-party plaintiff, may cause a summons and complaint to be served upon a person not a party to the action who is or may be liable to him for all or part of the plaintiff's claim against him. The third-party plaintiff need not obtain leave to make the service if he files the third-party complaint not later than 14 days after he serves his original answer. Otherwise he must obtain leave on motion upon notice to all parties to the action. The person served with the summons and third-party complaint, hereinafter called the third-party defendant, shall make his defenses to the third-party plaintiff's claim as provided in Rule 12 and his counterclaims against the third-party plaintiff and cross-claims against other third-party defendants as provided in Rule 13. The third-party defendant may assert against the plaintiff any defenses which the third-party plaintiff has to the plaintiff's claim. The third-party defendant may also assert any claim against the plaintiff arising out of the transaction or occurrence that is the subject matter of the plaintiff's claim against the third-party plaintiff. The plaintiff may assert any claim against the third-party defendant arising out of the transaction or occurrence that is the subject matter of the plaintiff's claim against the third-party plaintiff, and the third-party defendant thereupon shall assert his defenses as provided in Rule 12 and his counterclaims and cross-claims as provided in Rule 13. A third-party defendant may proceed under this rule against any person not a party to the action who is or may be liable to him for all or part of the claim made in the action against the third-party defendant.
(b) When plaintiff may bring in third party. When a counterclaim is asserted against a plaintiff, he may cause a third party to be brought in under circumstances which under this rule would entitle a defendant to do so.