We previously investigated the perception of noise-vocoded speech to determine whether the temporal amplitude envelope (TAE) of speech plays an important role in the perception of linguistic information as well as non-linguistic information. However, it remains unclear if these TAEs also play a role in the urgency perception of non-linguistic information. In this paper, we comprehensively investigated whether the TAE of speech contributes to urgency perception. To this end, we compared noise-vocoded stimuli containing TAEs identical to those of original speech with those containing TAEs controlled by low-pass or high-pass filtering. We derived degrees of urgency from a paired comparison of the results and then used them as a basis to clarify the relationship between the temporal modulation components in TAEs of speech and urgency perception. Our findings revealed that (1) the perceived degrees of urgency of noise-vocoded stimuli are similar to those of the original, (2) significant cues for urgency perception are temporal modulation components of the noise-vocoded stimuli higher than the modulation frequency of 6 Hz, (3) additional significant cues for urgency perception are temporal modulation components of the noise-vocoded stimuli lower than the modulation frequency of 8 Hz, and (4) the TAE of the time-reversal speech is not likely to contain important cues for the perception of urgency. We therefore conclude that temporal modulation cues in the TAE of speech are a significant component in the perception of urgency.