Open conflict broke out among U.S. liver transplant centers this week, with doctors and patients in less populous parts of the country seeking a contempt of court order against the Health and Human Services Department and the nonprofit organization that runs the transplant system.

Hospitals and patients on the waiting list for livers in places such as Georgia, Michigan, Kansas, Missouri and elsewhere accused the government and the United Network for Organ Sharing (UNOS) of defying a judge’s order to temporarily halt a new way of distributing those organs for transplant.

Atlanta federal court judge Amy Totenberg issued that order Wednesday night — a day after the new distribution rules went into effect — after deciding that the new policy would harm those patients, hospitals and the general public.

The doctors and patients claimed that transplant authorities were ignoring her order and asked that they be required “to show cause why they should not be held in contempt,” according to a court filing Thursday.

On Friday, Totenberg ordered the defendants to heed her order or face “sanctions and/or a contempt citation.” She scheduled a hearing for Monday to review whether the Department of Health and Human Services, which pays UNOS to run the transplant system, has complied.

Later Friday, UNOS issued a statement saying it would revert back to the previous rules. “Reprogramming this complex and important system is not a simple process and will take time to execute,” a spokeswoman said in the statement. “However, it is underway now and UNOS will have a greater sense of when the work will be completed next week.”

The legal skirmish is the latest in a decades-long struggle over how to allocate valuable livers, kidneys, hearts, lungs and other organs in a country where demand for transplants far exceeds supply.

Nearly 114,000 people are on the wait list for organs of all kinds. About three people die every day waiting for livers.

For years, transplant centers had first shot at livers procured from deceased donors in their regions. Over time, critics of that system say, huge geographic disparities developed, favoring places with smaller demand and larger supply.

For example, a moderately ill patient in Kansas has a 60 percent chance of receiving a liver in 30 days, while a similarly sick patient in California faces a 1 percent chance.

Last December, UNOS revamped the system to allow patients within 500 nautical miles of a donor’s hospital to claim a liver. Patients and transplant centers in less populous parts of the country sued in April, saying the new rules would allow big-city hospitals — where demand is highest — to reach far into their regions to take livers.

They contend the new policy will cut their access to livers by 20 percent or 256 livers, resulting in more deaths among patients in those areas.

After Totenberg blocked the new policy Wednesday, UNOS told liver transplant centers Thursday that the policy was still in effect. In court papers, lawyers told Totenberg it took months to adjust the computerized matching system that allocates organs nationwide and might take four weeks to reprogram it back.

On Friday, Totenberg told the government and UNOS to present witnesses at Monday’s hearing who can discuss those problems.