The temporal coherence of an injection-seeded transient 18.9 nm molybdenum soft x-ray laser was measured using a wavefront division interferometer and compared to model simulations. The seeded laser is found to have a coherence time similar to that of the unseeded amplifier, ~1 ps, but a significantly larger degree of temporal coherence. The measured coherence time for the unseeded amplifier is only a small fraction of the pulsewidth, while in the case of the seeded laser it approaches full temporal coherence. The measurements confirm that the bandwidth of the solid target amplifiers is significantly wider than that of soft x-ray lasers that use gaseous targets, an advantage for the development of sub-picosecond soft x-ray lasers.