No. European red deer (Cervus elaphus) and North American elk, also called wapiti (Cervus canadensis), are treated as separate species by most scientists today, even though they were long lumped together.
Yellowstone National Park notes that the taxonomy has been debated, but currently most scientists refer to North American elk as Cervus canadensis. Genetic studies also place elk closer to some Asian deer than to European red deer, and the two forms differ in traits such as rump-patch size and antler color.