An aircraft propulsion unit with an engine mount connecting a rigid casing, supporting a propeller, and a structure. First and second transverse link rods connect the casing and the structure with first and second joints each having an axis of pivoting substantially parallel to an axis of rotation of the propeller. First and second thrust rods connect the casing and the structure by first and second thrust rod connections. The first and second thrust rod connections separated from one another in the longitudinal direction. A longitudinal end stop is configured to limit the movement of the casing with respect to the structure in at least the longitudinal direction. An aircraft with at least one such propulsion unit.