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I believe the NTSB will investigate for US-registered aircraft accidents regardless of location, US-certified aircraft, accidents of foreign-registered aircraft in the US or its territories, or on any other accident upon request of another state.
Other main investigation offices:
Air Accidents Investigation: Home
Bureau d'Enquêtes et d'Analyses (BEA) - English Homepage
BFU - BEAA - UIIA - AAIB
Australian Transport Safety Bureau