Iran, North Korea, and Syria Nonproliferation Accountability Act of 2013

Prohibits U.S. nuclear cooperation agreements and related export licenses and transfers of materials, services and goods with a country that is assisting the nuclear program of Iran, North Korea, or Syria, or is transferring advanced conventional weapons to such countries.

Directs the President to submit an annual report to Congress that identifies each country that allows foreign persons under its jurisdiction to engage in sanctionable activities.

Directs the President to prohibit assistance (other than humanitarian assistance) under the Foreign Assistance Act of 1961 and not issue export licenses for defense articles or defense services under the Arms Export Control Act to a foreign country that is assisting Iran, North Korea, or Syria in the acquisition, development, or proliferation of weapons of mass destruction or ballistic missiles.

Prohibits any U.S. government agency from making extraordinary payments in connection with the International Space Station to the Russian Aviation and Space Agency or any other organization of the government of the Russian Federation unless the President has reported to Congress that: (1) it is Russian policy to oppose the proliferation to or from Iran, North Korea, and Syria of weapons of mass destruction and missile delivery systems; (2) the government of the Russian Federation has demonstrated a commitment to prevent the transfer to or from Iran, North Korea, and Syria of goods, services, and technology that could make a material contribution to Iran's nuclear, biological, chemical weapons, or missile programs; and (3) the Russian Aviation and Space Agency has not, during the one-year period ending on the date of such presidential determination, made transfers that are reportable under this Act to or from Iran, North Korea, or Syria.

Authorizes the National Aeronautics and Space Administration (NASA) to make extraordinary payments in connection with the International Space Station to the Russian Aviation and Space Agency that would otherwise be prohibited under this Act: (1) if such payments are necessary for crew safety aboard the International Space Station; or (2) for the construction, testing, preparation, delivery, launch, or maintenance of the Service Module, and for the purchase of the pressure dome for the Interim Control Module and the Androgynous Peripheral Docking Adapter for the U.S. propulsion module under specified conditions.

Directs the President to report to Congress identifying each Russian person or entity that the U.S. government has paid since November 22, 2005, for work to be performed or services to be rendered under the Agreement Concerning Cooperation on the Civil International Space Station or any related protocol, agreement, or contract.

Directs the Secretary of State to deny a visa to, and the Secretary of Homeland Security (DHS) to exclude from the United States, an alien listed in a report identifying persons involved in specified weapons proliferation activities with Iran.

Amends the Ports and Waterways Safety Act to require, before a vessel arrives at a U.S. port, the owner, charterer, operator, or master of the vessel to certify that the vessel did not enter a port in Iran, North Korea, or Syria during the 180-day period ending on the date of the vessel's U.S. port arrival.

Prohibits from landing in a U.S. port for at least two years: (1) any vessel for which a false certification was made; and (2) any other vessel owned or operated by a parent corporation, partnership, association, or individual proprietorship of the vessel for which the false certification was made.

Directs the Secretary (of the department in which the Coast Guard is operating) to: (1) identify foreign ports at which vessels have landed during the preceding 12-month period that have also landed at ports in Iran, North Korea, or Syria during such period; and (2) inspect vessels arriving in the United States from such foreign ports to establish whether a vessel was involved, during the 12-month period ending on the date of the vessel's U.S. arrival, in any activity that would be sanctionable under this Act.

Directs the President to apply foreign exchange, banking, property and loan guarantee sanctions to any person who provides to or acquires from Iran, North Korea, or Syria goods or technology that is used, or is likely to be used, for military applications.

Directs the Secretary of Energy, the Secretary of Commerce, and the Nuclear Regulatory Commission (NRC), before issuing an export license for nuclear cooperation or approving a loan guarantee or any other U.S. assistance with respect to a nuclear energy project, to certify to Congress that issuing the license or approving the loan guarantee will not permit the transfer of any goods or technology that may have military application to Iran, North Korea, or Syria.

Prohibits any U.S. contribution to the International Atomic Energy Agency (IAEA) from being used to support any assistance provided by the IAEA through its Technical Cooperation Program to Iran, North Korea, or Syria.

Repeals the Iran, North Korea, and Syria Nonproliferation Act.