In this paper we describe a procedure to obtain the general operator form of two-nucleon (2N) potentials and apply it to the case of the 2N potential that has an additional dependence on the total momentum of the system. This violates Galilean invariance but terms including the total momentum appear in some relativistic approaches. In operator form, the potential is expressed as a linear combination of a fixed number of known spin-momentum operators and scalar functions of momenta. Since the scalar functions effectively define the potentials, using the operator form significantly reduces the number of parameters that are needed in numerical implementations. The proposed operator form explicitly obeys the usual symmetries of rotational invariance, particle exchange, time reflection and parity.