We used the Nobeyama 45-m telescope to conduct a spectral line survey in the 3-mm band (85.1-98.4 GHz) toward one of the nearest galaxies with active galactic nucleus NGC 1068 and the prototypical starburst galaxy NGC 253. The beam size of this telescope is ~18, which was sufficient to spatially separate the nuclear molecular emission from the emission of the circumnuclear starburst region in NGC 1068. We detected rotational transitions of C2H, cyclic-C3H2, and H13CN in NGC 1068. These are detections of carbon-chain and carbon-ring molecules in NGC 1068. In addition, the C2H N = 1-0 lines were detected in NGC 253. The column densities of C2H were determined to be 3.4 x 10^15 cm^-2 in NGC 1068 and 1.8 x 10^15 cm^-2 in NGC 253. The column densities of cyclic-C3H2 were determined to be 1.7 x 10^13 cm^-2 in NGC 1068 and 4.4 x 10^13 cm^-2 in NGC 253. We calculated the abundances of these molecules relative to CS for both NGC 1068 and NGC 253, and found that there were no significant differences in the abundances between the two galaxies. This result suggests that the basic carbon-containing molecules are either insusceptible to AGN, or are tracing cold (T_rot ~10 K) molecular gas rather than X-ray irradiated hot gas.