The bodies were found in three locations in Guerrero and Michoacan states, the Los Angeles Times reported.
The newspaper said Mexican military troops have been deployed in both states in an attempt to stem the tide of violence linked to drug cartels and local militias that have been formed to try to protect communities in the region.
Eight bodies were found in Los Cajones. The Guerrero state attorney general's office said five men in military-style clothing were found shot in a pickup truck and the bodies of three other men also were found, presumably nearby.
Eight more bodies was found in Taxco de Alarcon, Guerrero state, the Times said the news service Milenio reported.
Nine bodies were found in Tepalcatepec, Michoacan state, and the Times said the newspaper El Universal reported there were indications they had been tortured.