The Department of State, which is the agency responsible for processing visa applications outside the U.S., posted this alert yesterday:
“The U.S. government's national security screening and vetting procedures for visitors are constantly reviewed and refined to improve security and more effectively identify individuals who could pose a threat to the United States. We welcome every opportunity to continue to review and improve our systems and procedures. As a result of this executive order, the Department of State has temporarily stopped scheduling appointments and halted processing of immigrant and nonimmigrant visa applications for individuals who are nationals of Syria, Iraq, Iran, Libya, Somalia, Sudan, and Yemen.
This Executive Order does not restrict the travel of dual nationals from any country with a valid U.S. visa in a passport of an unrestricted country. Our Embassies and Consulates around the world will continue to process visa applications and issue nonimmigrant and immigrant visas to otherwise eligible visa applicants who apply with a passport from an unrestricted country, even if they hold dual nationality from one of the seven restricted countries. Please check with your local Embassy or Consulate for country specific information.”
In other words, if you are national of banned country and a country that is not banned, you may be eligible for a visa and entry into the U.S.
Of course, you should check with an immigration attorney for your specific situation, before taking any action.