Denying Firearms and Explosives to Dangerous Terrorists Act of 2013 - Amends the federal criminal code to authorize the Attorney General to deny the transfer of a firearm or the issuance of a firearms or explosives license or permit (or revoke such license or permit) if the Attorney General: (1) determines that the transferee is known (or appropriately suspected) to be engaged in terrorism or has provided material support or resources for terrorism; and (2) has a reasonable belief that the transferee may use a firearm in connection with terrorism. Allows any individual whose firearms or explosives license application has been denied to bring legal action to challenge the denial.

Extends the prohibition against the sale or distribution of firearms or explosives to include individuals whom the Attorney General has determined to be engaged in terrorist activities. Imposes criminal penalties on individuals engaged in terrorist activities who smuggle or knowingly bring firearms into the United States.

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