The Justice Department asked the federal judge overseeing its settlement on CVS Health Corp.'s $69 billion acquisition of Aetna Inc. to throw out what it calls “irrelevant” testimony from the deal’s opponents because it could threaten the government’s ability to regulate future mergers.

The DOJ approved the merger in October once Aetna agreed to sell its Medicare Part D drug plan business. CVS, one of the nation’s largest pharmacy service providers, and health insurance giant Aetna closed the deal in November.

The DOJ’s settlement hit a snag April 8 when Judge Richard Leon of the U.S. District Court for the...