Intergovernmental Critical Minerals Task Force Act This bill directs the Office of Management and Budget (OMB) to establish a task force to facilitate cooperation, coordination, and mutual accountability among each level of the federal government and state, local, tribal, and territorial governments on a holistic response to the dependence on covered countries for critical minerals across the United States. Covered country includes any country determined by the task force to be a geostrategic competitor or adversary of the United States with respect to critical minerals. The bill specifies duties for the task force, including addressing the homeland and national security risks associated with the current critical mineral supply chains of the United States; identifying a list of critical minerals most important for securing U.S. homeland and national security; and providing recommendations addressing research and development, mining, and strengthening the domestic workforce to support, and improving partnerships with allied countries to improve, critical mineral supply chains.