This work investigates the position control problem for a soft continuum manipulator in Cartesian space intended for minimally invasive surgery. Soft continuum manipulators have a large number of degrees-of-freedom and are particularly susceptible to external forces because of their compliance. This, in conjunction with the limited number of sensors typically available, results in uncertain kinematics, which further complicates the control problem. We have designed a partial state feedback that compensates the effects of external forces employing a rigid-link model and a port-Hamiltonian approach and we have investigated in detail the use of integral action to achieve position regulation in Cartesian space. Local stability conditions are discussed with a Lyapunov approach. The performance of the controller is compared with that achieved with a radial-basis-functions neural network by means of simulations and experiments on two prototypes.