We apply the strong pi NN form factor, which emerges from the Skyrme model, in the two-nucleon system using a one-boson-exchange (OBE) model for the nucleon-nucleon (NN) interaction. Deuteron properties and phase parameters of NN scattering are reproduced well. In contrast to the form factor of monopole shape that is traditionally used in OBE models, the Skyrme form factor leaves low-momentum transfers essentially unaffected while it suppresses the high-momentum region strongly. It turns out that this behavior is very appropriate for models of the NN interaction and makes it possible to use a soft pion form factor in the NN system. As a consequence, the pi N and the NN systems can be described using the same pi NN form factor, which is impossible with the monopole.