The appellate court, which is expected to rule on the preventive care mandate’s constitutionality later this year, still has to approve the lawyers’ agreement.

Health policy experts describe the mandate as one of the most transformative policies of the health law, known as Obamacare, because it could prevent worsening disease and higher costs later on. It is also popular, with 62 percent of the public recently saying it was “very important” that it stay in place.

Before the Affordable Care Act’s passage, in March 2010, patients sometimes faced big bills for preventive care such as birth control or colonoscopies. Since the mandate took effect, studies have shown, more Americans have received blood pressure screenings, cholesterol screenings and flu vaccines.

In March, Judge Reed O’Connor of the Federal District Court for the Northern District of Texas ruled that part of the mandate was unconstitutional because an independent panel advising the government on what benefits to cover did not have the proper authority to do so.

Judge O’Connor’s ruling did not undo the entire preventive services mandate, but said it should not cover services that the panel, the United States Preventive Service Task Force, had recommended since 2010.