The combination of small-cluster exact-diagonalization calculations and the quantum Monte Carlo method is used to examine ferromagnetism in the two-dimensional Hubbard model with a generalized type of hopping. It is found that the long-range hopping with exponentially decaying hopping amplitudes t
ij ∼ − q
Ri−Rj stabilizes the ferromagnetic state for a wide range of electron interactions U and electron concentrations n > 1. The critical value of the hopping parameter q
c above which the ferromagnetic state becomes stable is calculated numerically and the ground-state phase diagram of the model is discussed for physically the most interesting cases.