Context. Known TeV sources detected by major Cerenkov telescopes are investigated to identify possible MeV-GeV gamma-ray counterparts. Aims. A systematic study of the known sources in the web-based TeVCat Catalog has been performed to search for possible gamma-ray counterpart on the AGILE data collected during the first period of operations in observing pointing mode. Methods. For each TeV source, a search for a possible gamma-ray counterpart based on a multi-source Maximum Likelihood algorithm is performed on the AGILE data taken with the GRID instrument from July 2007 to October 2009. Results. In case of high-significance detection, the average gamma-ray flux is estimated. For the cases of low-significance detection the 95 % Confidence Level (C.L.) flux upper limit is given. 52 TeV sources out of 152 (corresponding to ~34 % of the analysed sample) show a significant excess in the AGILE data covering the pointing observation period. Conclusions. This analysis found 26 new AGILE sources with respect to the AGILE reference catalogs, 15 of which are Galactic, 7 are extragalactic and 4 are unidentified. Detailed tables with all available information on the analysed sources are presented.