The low-temperature quantum transport properties of gated InN nanowires were investigated. Magnetic-field-dependent as well as gate-dependent measurements of universal conductance fluctuations were performed to gain information on the phase coherence in the electron transport. We found a pronounced decrease in the variance of the conductance by about a factor of 2 in gate-dependent fluctuation measurements if a magnetic field is applied. This effect is explained by the suppression of the Cooperon channel of the electron correlation contributing to the conductance fluctuations. Despite the fact that the diameter of the nanowire is less than 100 nm a clear weak antilocalization effect is found in the averaged magnetoconductance being in strong contrast to the suppression of weak antilocalization for narrow quantum wires based on planar two-dimensional electron gases. The unexpected robustness of the …