The aircraft was flying to the Loisaba Conservancy, a wildlife reserve and safari destination in northern Kenya, when it crashed, according to a preliminary report from Archers Post police station seen by Reuters.
All seven people - six passengers and one pilot - were killed, authorities said.
A State Department spokesperson said five Americans were among the dead, while Ecuador's presidential office confirmed intelligence head Michele Sensi-Contugi and his wife Stephany Hollihan - who held U.S. citizenship - were also killed.
"The U.S. Embassy is in touch with local authorities and is providing consular assistance," the State Department said.
The preliminary police report listed Sensi-Contugi and his wife as tourists.
Luxury tour agency &Beyond, which offered the excursion the tourists were on, said in a statement that the cause of the crash was yet to be determined.
The Kenya Red Cross said that search and recovery efforts were being hampered by difficult terrain and a fire at the crash site.
(Reporting by Humphrey Malalo, Vincent Mumo Nzilani and Ammu Kannampilly in Nairobi, Elias Biryabarema in Kampala and Nilutpal Timsina in Johannesburg; Additional reporting by Alexandra Valencia in Quito; Writing by Kylie Madry; Editing by Alexander Winning, Alex Richardson and Alistair Bell)