14 CFR 61.3 (Requirement for certificates, ratings, and authorizations)
(a) Required pilot certificate for operating a civil aircraft of the
United States. No person may serve as a required pilot flight
crewmember of a civil aircraft of the United States, unless that
person:
...
(vii) When operating an aircraft within a foreign country, a pilot
license issued by that country may be used.
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The FAA Assistant Chief Counsel for Regulations, Mark W Bury, provided an interpretation of the term "foreign country" on 9 Feb 2015 to Luc Audoore, CAE Aviation:
You have asked whether “within a foreign country” refers to the legal borders of a country
(i.e. landmass and territorial waters) or the Flight Information Region that would include the
sea outside the territorial waters.
The FAA is required to act consistently with U.S. obligations under international
agreements. 49 U.S.C. § 40105 (b). The Chicago Convention uses the term “State” rather
than “country” when addressing a contracting State’s responsibilities. Under Article 2 of the
Chicago Convention, a State’s territory is "deemed to be the land areas and territorial waters
adjacent thereto under the sovereignty, suzerainty, protection, or mandate of such State." As
such, the FAA considers operation “within a foreign country” to be operation within the
territory of a State. Although a country may be responsible for providing navigation services
outside its territory, the FAA would not consider operations of a U.S-registered airplane in
those areas to be an operation “within that country” for the purpose of § 61.3. Thus, the
operation described in your request would require the pilot to hold a pilot certificate issued
by the FAA.