This research presents an investigation of the feasibility of recycled polyethylene terephthalate (rPET) and glycol-modified polyethylene terephthalate (rPETG) thermoplastics using the fused granular fabrication (FGF) 3D printing technique. It focuses on the effects of FGF printing parameters on the mechanical properties of rPET and rPETG printed parts using a Gigabot X 3D printer. The design of experiments (DOE) was first performed considering the main FGF 3D printing parameters such as layer thickness, infill density and number of contours. The experimental studies were then carried out to study the effects of printing parameters on the tensile properties based on the DOE. The effect of interlayer bonding of printed parts on the tensile properties was also evaluated using finite element-based multiscale modelling. Scanning electron microscopy (SEM) and Fourier transformation infrared (FTIR) spectroscopy were used to observe the fracture morphology and chemical structure of post-FGF printing products. The tensile test results indicate that the highest tensile strength of 26.4 MPa was obtained for rPET when using a 1.1-mm layer thickness, a 70% infill density, and 3 contours, whereas, for rPETG, the maximum tensile strength of 44.8 MPa was attained with a 1.2-mm layer thickness, a 100% infill density, and 2 contours. FTIR analysis confirms no significant changes of characteristic peaks for PET in the printed products, suggesting that rPET and rPETG are viable materials for FGF printing. Thermal stability studies also reveal that the glass transition temperature and onset degradation temperatures are not significantly affected by the printing parameters. The study demonstrates the potential of rPET and rPETG as sustainable alternatives to virgin materials and provides insights into the optimal processing conditions for achieving high-quality 3D printed parts via the FGF technique.