Highly accurate group delay measurements in long single-mode fibers were achieved over the full 1200-1600 nm spectral range by measuring phase shifts of a modulated lightwave. The high modulation frequency is shifted down to the kilohertz range using a second optical modulation at the fiber output end, so that low-frequency, ultrasensitive detection and phase measurement can be performed with high-frequency resolution conserved. This results in extremely reliable measurements with a <1-ps resolution using a fully remote light source such as an LED or even a halogen lamp.