A superconducting state is characterized by the gap in the electronic density of states, which vanishes at the superconducting transition temperature T(c). It was discovered that in high-temperature superconductors, a noticeable depression in the density of states, the pseudogap, still remains even at temperatures above T(c). Here, we show that a pseudogap exists in a conventional superconductor, ultrathin titanium nitride films, over a wide range of temperatures above T(c). Our study reveals that this pseudogap state is induced by superconducting fluctuations and favoured by two-dimensionality and by the proximity to the transition to the insulating state. A general character of the observed phenomenon provides a powerful tool to discriminate between fluctuations as the origin of the pseudogap state and other contributions in the layered high-temperature superconductor compounds.