Trying to devise a one-size-fits-all description for ultraprocessed foods is flummoxing federal regulators.

For months, the health secretary, Robert F. Kennedy Jr., has promised to create a definition of ultraprocessed, a crucial part of the Make America Healthy Again agenda. In mid-April, he testified before Congress that the Food and Drug Administration had forwarded a definition to other agencies, including the Department of Agriculture.

But behind the scenes, officials said, the process of defining ultraprocessed foods is still very much up in the air.…