In 2012, the U.S. Department of State made international news when it refused to issue proof of U.S. Citizenship to the newborn baby of a U.S. Citizen mother. The mother had carried the baby to term, but due to issues conceiving, she had carried the fertilized egg of another woman to term. (In today's terms, she might be called a gestational mother.) The Department of State determined that since the biological mother and father of the child (the egg and sperm donors) were not U.S. citizens, the child was not a U.S. Citizen.
The Department of State has now issued guidance on the use of Assisted Reproductive Technology (ART) by U.S. Citizens abroad. The Department's interpretation of the law on transmission of citizenship by parents to their children is that a parent must have a "biological connection" to the child. A biological parent has a biological connection to a child, and according to the new guidance, a woman who carries a baby to term also has a biological connection to the child for purposes of transmitting citizenship.
The Department of State makes the determination on the transmission of U.S. citizenship from parent to child based on U.S. laws. Local laws do not affect this determination.
The full guidance is available at: http://travel.state.gov/content/travel/english/legal-considerations/us-citizenship-laws-policies/assisted-reproductive-technology.html