Wayne Cooper, 70, makes his way indoors in McClean, Va., on Dec. 29, 2017. Cooper was recovering from transplant surgery after his daughter, Patricia, donated part of her liver to him. (Salwan Georges/The Washington Post)

The Trump administration on Tuesday extended the deadline to bid for the contract to run the nation’s organ transplant system after potential competitors complained that previous rules strongly favored the current operator, the United Network for Organ Sharing (UNOS).

A notice on the website FedBizOpps.gov announced the extension of the bidding period from May 4 to May 30. That gives anyone who wants to bid for the contract 60 days from March 30, when the request for proposals was first announced.

Potential bidders were initially given just 31 days to respond. The deadline was later postponed by four days, to May 4.

UNOS, a nonprofit organization, is the only entity ever to hold that contract. It has faced only occasional competition over the past 32 years for the right to run the complex system that connects organ donors with recipients nationwide. No one has sought to compete with UNOS since at least 2005, which is as far back as relevant government records go.

A spokesman for the federal Health Resources and Services Administration, which oversees UNOS and the transplant system, had no comment. Previously, the agency, which is part of the Department of Health and Human Services, said that information released last year about the contract gave potential bidders enough time to put together their own plans.

Members of two nonprofit groups that have expressed interest in competing for the contract did not respond to requests for comment Tuesday.

But both have said previously that the rules for the competition strongly favor UNOS. They said that designing a complex plan to govern more than 800 transplant programs and the organizations that serve them is nearly impossible in just 35 days.

The government also is requiring bidders to have three years’ experience managing transplant programs of similar complexity — a description, one group asserted, that fits only UNOS. And if any of the aspirants does win the contract, that organization would not inherit UNOS’s software or computer equipment, the guts of a complicated network that sometimes must match donors with faraway recipients in just a few hours.

The contract’s price tag is uncertain, but federal tax records show that UNOS collected nearly $58 million in 2015, most of it from the fees patients pay to be placed on waiting lists. As of Tuesday, 114,855 people were on waiting lists for kidneys, livers, hearts, lungs and other organs. Some have been waiting for years because of the country’s severe shortage of transplant organs.