Countering ALBA Act of 2013 - Requires the Secretary of State to direct the U.S. Permanent Representative to the Organization of American States to use the voice, vote, and influence of the United States to defend, protect, and strengthen the independent Inter-American Commission on Human Rights to advance the protection of human rights throughout the Western Hemisphere.

Directs the President to impose sanctions against certain listed officials of ALBA governments (Venezuela, Nicaragua, Bolivia, and Ecuador) or persons acting on behalf of ALBA governments who the President determines are responsible for, or complicit in, the commission of serious human rights abuses against citizens of ALBA countries or their family members on or after February 2, 1999. Includes among authorized sanctions ineligibility for a U.S. entry visa and sanctions pursuant to the International Emergency Economic Powers Act. Terminates such sanctions when the President determines and certifies to the congressional foreign relations committees that the ALBA governments have: (1) unconditionally released all political prisoners; (2) ceased violence, unlawful detention, torture, and abuse of its citizens; (3) conducted a transparent investigation into the killings, arrests, and abuse of peaceful political activists, and prosecuted those responsible; and (4) made public commitments to, and are making demonstrable progress toward, establishing an independent judiciary and respecting the human rights and basic freedoms recognized in the Universal Declaration of Human Rights.

Directs the President to impose sanctions against listed individuals who transfer goods or provide services to ALBA countries that are likely to be used to commit serious human rights abuses.

Directs the President to impose sanctions against listed persons who engage in censorship or other related activities against citizens of ALBA countries.

Directs the Secretary of State to submit to the foreign relations committees a comprehensive strategy: (1) to assist the people of ALBA countries in promoting Internet freedom and access to information, and (2) to ensure that ALBA governments are democratic governments.