Denying Firearms and Explosives to Dangerous Terrorists Act of 2013 - Amends the federal criminal code to grant the Attorney General the authority to deny the transfer of firearms or the issuance of a federal firearms and explosives license to any individual if the Attorney General: (1) determines that such individual has been engaged in or has provided material support or resources for terrorist activities, and (2) has a reasonable belief that such individual may use a firearm or explosive in connection with terrorism. Allows any individual whose firearm or explosives license application has been denied to bring legal action challenging the denial.

Prohibits the sale or distribution of firearms or explosives to any individual whom the Attorney General has determined to be engaged in terrorist activities.

Permits the Attorney General to withhold information in firearms and explosives license denial revocation suits if the Attorney General determines that the disclosure of such information would likely compromise national security.

Authorizes the Attorney General to revoke firearms and explosives licenses and permits held by individuals determined to be engaged in terrorism.