National All Schedules Prescription Electronic Reporting Reauthorization Act of 2013

National All Schedules Prescription Electronic Reporting Reauthorization Act of 2013 - Amends the National All Schedules Prescription Electronic Reporting Act of 2005 to include as a purpose of such Act to foster the establishment of state-administered controlled substance monitoring systems in order to ensure that appropriate law enforcement, regulatory, and state professional licensing authorities have access to prescription history information for the purposes of investigating drug diversion and prescribing and dispensing practices of errant prescribers or pharmacists.

Amends the Public Health Service Act to revise and update the controlled substance monitoring program, including to: (1) allow grants to be used to maintain and operate existing state controlled substance monitoring programs, (2) require the Secretary of Health and Human Services (HHS) to redistribute any funds that are returned among the remaining grantees, (3) require a state to provide the Secretary with aggregate data and other information to enable the Secretary to evaluate the success of the state's program and to submit a progress report to Congress, and (4) expand the program to include any commonwealth or territory of the United States.

Authorizes the Drug Enforcement Administration (DEA) or a state Medicaid program or state health department receiving nonidentifiable information from a controlled substance monitoring database to make such information available to other entities for research purposes.

Requires a state receiving a grant to: (1) facilitate prescriber use of the state's controlled substance monitoring system, and (2) educate prescribers on the benefits of the system both to them and society.

Revises preferences for grants related to drug abuse to authorize the Secretary to give preference to eligible states or tribes that put forth a good faith effort to meet minimum requirements under the controlled substance monitoring program.