A lawsuit accusing General Electric Co. of monopolizing the market for servicing of its anesthesia machines will pause as the two sides undergo court-ordered mediation.

The GE servicing agreements signed by the hospital plaintiffs included dispute resolution clauses that clearly encompass their antitrust claims, “which makes mediation the ticket of admission to litigation,” Judge Richard G. Stearns, of the U.S. District Court for the District of Massachusetts, ruled May 6.

Hospitals in Texas and Alabama filed the proposed class suit,...