We present a study of 40 low-latitude unidentified 3EG gamma-ray sources which were found to be not positionally coincident with any known class of potential gamma-ray emitters in the Galaxy (Romero et al., 1999A&A...348..868R). We have performed a variability analysis which reveals that many of these 40 sources are variable. These sources have, in addition, a steep mean value of the gamma-ray spectral index, <{Gamma}>=2.41+/-0.2, which, combined with the high level of variability, seems to rule out a pulsar origin. The positional coincidences with uncatalogued candidates to supernova remnants were also studied. Only 7 sources in the sample are spatially coincident with these candidates, a result that is shown to be consistent with the expected level of pure chance association. A complementary search for weak radio counterparts was also conducted and the results are presented as an extensive table containing all significant point-like radio sources within the 40 EGRET fields. We argue that in order to produce the high variability, steep gamma-ray spectra, and absence of strong radio counterparts observed in some of the gamma-ray sources of our sample, a new class of objects should be postulated, and we analyze a viable candidate.