A potential resolution to a lingering debate on how the government should oversee laboratory-developed diagnostic tests would focus the FDA’s attention on the more cutting-edge and riskier screening tools.

At issue is a disagreement between device companies and clinical laboratory groups on what constitutes appropriate federal oversight of laboratory-developed test (LDTs), which are developed in a single laboratory, compared to the same type of diagnostics made by device companies.

Scott Gottlieb, commissioner of the Food and Drug Administration, unveiled Sept. 13 a proposal for how his agency could regulate in vitro diagnostic tests, or tests on bodily samples, that...