An approximate theory is developed for the two-dimensional propagation of tsunami emanated from a slender fault of fine length. Assuming significant contrasts between the sea depth, fault width, fault length and the bathymetric length scales, we invoke parabolic approximation to deduce a linear Kademtsev-Petviashivili (K-P) equation governing the two-dimensional propagation of dispersive long waves over great distances. Analytical techniques are employed to explore the far-field radiation in the forward and spanwise directions in a sea of constant depth. The solution can be used as a convenient input for predicting local variations of wave scattering and possibly breaking along a coast.