National Forest Insect and Disease Treatment Act of 2013 - Amends the Healthy Forests Restoration Act of 2003 to direct the Secretary of Agriculture (USDA) or the Secretary of the Interior, as appropriate, to designate as part of an insect and disease treatment and research pilot program at least one subwatershed in at least one national forest in each state that is experiencing an insect or disease epidemic and characterized by: (1) substantially increased tree mortality due to infestation; (2) the risk of substantially increased tree mortality over the next 15 years due to infestation; or (3) presence in an area in which the risk of hazard trees poses an imminent risk to public infrastructure, health, or safety.

Authorizes the Secretary to carry out priority projects on federal land in the designated subwatersheds to reduce the risk or extent of, or increase the resilience to, insect or disease infestation in the subwatersheds. Deems such projects to be authorized hazardous fuel reduction projects.

Extends the authorization of appropriations for the insect infestation and related diseases program through FY2018.