In seismology numerous observations indicate a relationship between pore pressure in the Earth's crust and the occurrence of earthquakes. In this paper we study aftershock sequences in the South Iceland Seismic Zone (SISZ), where poroelastic rebound has been observed in the post-seismic period of two M 6.5 earthquakes in 2000 June. We analyse characteristic features in the spatiotemporal distribution of aftershocks following the two M 6.5 2000 June 17 and 21 earthquakes and a M 4.5 earthquake on 1999 September 27. These features include an initial pre-power-law decay period characterized by an initially finite aftershock rate, a subsequent power-law decay interrupted by distinct and temporary rate increases and decreases as well as increased clustering of aftershocks with time in the main shock fault zones. Extending the analysis to a M 3.2 aftershock sequence in the same region confirms an increase in the duration of the initial pre-power-law decay period with increasing main shock magnitude. We find, from the return time of aftershock magnitudes to the long-term completeness level, that the initial pre-power-law decay period and its durational dependence on main shock magnitude may not only represent incompleteness artefacts but may also reflect the physics of the aftershock process in the SISZ. Based on pore pressure diffusion modelling, we interpret the origin of the observed SISZ aftershock features in terms of a spatially non-linear coseismic influence of the main shock on stresses in the surrounding crust and poroelastic adjustment of stresses and pore pressures during main shock initiated diffusion processes. In a discussion of alternative interpretations, we find that rate and state friction and dynamically propagating crack models, the statistical ETAS model, afterslip models, viscoelastic relaxation of the lower crust and upper mantle and a recently proposed dependence on the crustal state of stress all appear inconsistent with at least one of the characteristic spatiotemporal features of the studied SISZ aftershock sequences. We conclude that these features constitute strong evidence for pore pressure effects in aftershock triggering within the SISZ and recommend that poroelastic adjustment of stresses is taken into account in modelling of main shock initiated pore pressure diffusion.