Herein, we report magnetic properties of as-synthesized face centered cubic (fcc)-FePt nanoparticles (∼5 nm) and its transformed face centered tetragonal (fct) phase when annealed at 600 °C. We observe weak ferromagnetic nature in fcc phase with non-saturating M-H loop indicating the presence of a large fraction of superparamagnetic particles. Excess of Fe-precursor with respect to Pt used in the reaction accumulates on the surface of the FePt nanoparticles and forms a thin layer of Fe-byproduct (Fe3O4) which leads to the formation of FePt/Fe3O4 core/shell structure. This was confirmed by X-ray diffraction, X-ray photoelectron spectroscopy, and microstructural studies. Interestingly due to core/shell formation, the coercivity (Hc) is higher at 300 K than at 50 and 100 K, but there is a steep increase at 5 K. Moreover, hysteresis loop is regular at 300 K whereas it is distorted at 5 K. The reason for temperature dependent Hc anomaly and distortion in M-H loop was examined systematically. The competing exchange interaction seems to be responsible for changes in the magnetic behavior. Besides this, it shows spin glass like behavior much below the blocking temperature which is supposed to be due to existence of two magnetic phases and the exchange coupling between core and shell. This has been confirmed from temperature dependent dc magnetization and ac susceptibility studies. We establish a clear correlation between the magnetization dynamics and the core/shell structure of the nanoparticles. On the other hand, the fct phase shows a very large coercivity with some irregularity in the M-H loop. This irregularity may be ascribed due to segregation of fcc-Fe3Pt (soft) phase on the grain boundaries of fct-FePt (hard). Such inhomogeneity in bimagnetic systems (soft–soft or soft–hard) has strong influence on the nanomagnetism.