On-chip manipulation of the spatiotemporal characteristics of optical signals is important in the transmission and processing of information. However, the simultaneous modulation of on-chip optical pulses, both spatially at the nano-scale and temporally over ultra-fast intervals, is challenging. Here, we propose a two-dimensional spatiotemporal Fourier transform (FT) method for on-chip control of the propagation of femtosecond optical pulses and verify this method employing surface plasmon polariton (SPP) pulses on metal surface. By varying space- and frequency-dependent parameters, we demonstrate that the traditional SPP focal spot may be bent into a ring shape, and that the direction of propagation of a curved SPP-Airy beam may be reversed at certain moments to create an S-shaped path. Compared with conventional spatial modulation of SPPs, this method offers potentially a variety of extraordinary effects in SPP modulation especially associated with the temporal domain, thereby providing a new platform for on-chip spatiotemporal manipulation of optical pulses with applications including ultrafast on-chip photonic information processing, ultrafast pulse/beam shaping, and optical computing.