Congressional Oversight of Afghanistan Agreements Act of 2013 - Directs the Legal Advisor to the Secretary of State to submit to Congress an unclassified report providing the justification for the President's decision to deny Congress its constitutionally protected role by concluding an agreement on the future of the security relationship between the United States and Afghanistan as an executive agreement.
Requires such report to include a legal analysis of the constitutional powers asserted by the President in concluding that such an agreement does not require congressional approval.
Expresses the sense of Congress that any bilateral agreement between the United States and Afghanistan involving commitments or risks affecting the nation as a whole, including a Bilateral Security Agreement, that is not a treaty approved by two-thirds of the Senate under Article II of the Constitution or authorized by legislation does not have the force of law.
Prohibits funds from being authorized or appropriated to carry out any bilateral agreement between the United States and Afghanistan involving commitments or risks affecting the nation as a whole, including a Bilateral Security Agreement, that is not a treaty approved by two-thirds of the Senate under Article II of the Constitution or authorized by legislation passed by both houses of Congress.