High-pressure x-ray-diffraction studies have been carried out upto 20 GPa on iron-filled multiwalled carbon nanotubes (MWNTs). The pressure dependence of the intertubular spacing d₀ of the filled MWNTs shows a sharp change at 9 GPa which is not observed in pristine MWNTs. The iron present as nanowires inside the MWNT is in the form of α-Fe and Fe3C. Both of these phases show higher compressibility than their bulk form. Most interestingly, the structural modification of MWNTs at 9 GPa coincides with an iso-structural phase transition in the encapsulated Fe₃C, in sharp contrast to the absence of a transition in the bulk Fe₃C upto 70 GPa.