The fuel injection pump arrangement for a dual-fuel internal combustion engine comprises a pump body (1), at least one fuel chamber (10) that is arranged inside the pump body (1), at least one reciprocating plunger (2) that protrudes into the fuel chamber (10) for pressurizing liquid fuel in the chamber (10), a plunger moving mechanism (5, 11) for establishing mechanical connection between the plunger (2) and a rotating cam that drives the fuel injection pump, and means (4, 6, 7) for breaking the mechanical connection between the plunger (2) and the cam when the fuel injection pump is not used for pressurizing fuel. The invention also concerns a method for operating a dual-fuel engine.