International Conflicts of Concern Act This bill directs the President to identify to Congress each country whose government is, and each country in which anti-government forces are, allowing one or more foreign terrorist organizations to engage in armed conflict occurring in that country. The President shall designate a country as a "country of conflict concern" if: (1) its government or anti-government forces in the country are allowing one or more foreign terrorist organizations to engage in armed conflict in it, and (2) it is in the U.S. national security to restrict travel by any U.S. national to the country and restrict material support by U.S. nationals of entities engaged in armed conflict in it. Such a designation shall be terminated when the President certifies to Congress that either or both of these circumstances no longer apply. The bill deems Syria to be a country of conflict concern. The Presidentshall require a U.S. national to obtain a license to: (1) travel to a country of conflict concern, or (2) provide material support to entities engaged in armed conflict in such a country. Specified penalties shall apply to a person who violates such requirements.