Permanent Stewardship Contracting Authority Act of 2013 - Amends the Healthy Forests Restoration Act of 2003 to authorize the Forest Service and the Bureau of Land Management (BLM) to enter into stewardship contracting projects with private persons or other public or private entities to perform services to achieve land management goals for the national forests and public lands that meet local and rural community needs.

States that the land management goals of a project may include: (1) road and trail maintenance or obliteration to restore or maintain water quality; (2) soil productivity, habitat for wildlife and fisheries, or other resource values; (3) setting of prescribed fires to improve the composition, structure, condition, and health of stands or to improve wildlife habitat; (4) removing vegetation or other activities to promote healthy forest stands, reduce fire hazards, or achieve other land management objectives; (5) watershed restoration and maintenance; (6) restoration and maintenance of wildlife and fish; or (7) control of noxious and exotic weeds and reestablishing native plant species.

Repeals a section of the Department of the Interior and Related Agencies Appropriations Act, 1999 that provides for forest health protection.