The URu2-xRexSi2 system exhibits ferromagnetic order for Re concentrations 0.3 < x < or =1.0. Non-Fermi-liquid (NFL) behavior is observed in the specific heat for 0.15< or = x< or =0.6 [C/T proportional to, -lnT (or T(-0.1))], and also in the power-law T dependence of the electrical resistivity [rhoT proportional to, Tn] with n<2 for 0.15< or = x <0.8, at low T, providing strong evidence that the NFL behavior persists within the ferromagnetic phase. Furthermore, the deviation of the physical properties of URu2-xRexSi2 from Fermi-liquid behavior is most pronounced at the ferromagnetic quantum critical point, and the NFL behavior found in the ferromagnetic phase may be consistent with the Griffiths-McCoy phase model.