Semiconductor nano-lasers grown on silicon and emitting at the telecom bands are advantageous ultra-compact coherent light sources for potential Si-based photonic integrated circuit applications. However, realizing room-temperature lasing inside nano-cavities at telecom bands is challenging and has only been demonstrated up to the E band. Here, we report on InP/InGaAs nano-ridge lasers with emission wavelengths ranging from the O, E, and S bands to the C band operating at room temperature with ultra-low lasing thresholds. Using a cycled growth procedure, ridge InGaAs quantum wells inside InP nano-ridges grown on patterned (001) Si substrates are designed as active gain materials. Room-temperature lasing at the telecom bands is achieved by transferring the InP/InGaAs nano-ridges onto a SiO2/Si substrate for optical excitation. We also show that the operation wavelength of InP/InGaAs nano-lasers can be adjusted by altering the excitation power density and the length of the nano-ridges formed in a single growth run. These results indicate the excellent optical properties of the InP/InGaAs nano-ridges grown on (001) Si substrates and pave the way towards telecom InP/InGaAs nano-laser arrays on CMOS standard Si or silicon-on-insulator substrates.