Aims. We present high-resolution spectroscopy of a number of planetary nebulae (PNe) and H ii regions distributed along the dwarf irregular galaxy NGC 3109 and compare their kinematical behavior with that of H i data. We aim to determine if there is a kinematical connection among these objects. We also aim to determine the chemical composition of some PNe and H ii regions in this galaxy and discuss it in comparison with stellar evolution models.Methods. Data for eight PNe and one H ii region were obtained with the high-resolution spectrograph Magellan Inamori Kyocera Echelle (MIKE) at Las Campanas Observatory, Chile. Data for three PNe, six compact H ii regions, and nine knots or clumps in extended H ii regions were obtained with the high-resolution spectrograph Manchester Echelle Spectrometer (MES) attached to the 2.1m telescope at the Observatorio Astronómico Nacional, SPM, B.C., Mexico. An additional object was obtained from The SPM Catalogue of Extragalactic Planetary Nebulae. Thus, in total we have high-quality data for nine of the 20 PNe detected in this galaxy, and many H ii regions. In the wavelength calibrated spectra, the heliocentric radial velocities were measured with a precision better than 7.8 km s −1 . Data for blue supergiant stars were collected from the literature to be included in the analysis. The heliocentric radial velocities of the different objects were compared to the velocities of the H i disk at the same position. Physical conditions and ionic abundances of PNe and H ii regions were obtained from the emission lines, and we used recent ionization correction factors to derive the total chemical abundances.Results. From the analysis of radial velocities we found that H ii regions in NGC 3109 share the kinematics of the H i disk at the same projected position with very low dispersion in velocities. Blue supergiant stars and PNe rotate in the same direction as the H i disk but these objects have much larger dispersion; this larger dispersion is possibly because these objects belong to a different population that is located in the central stellar bar reported for this galaxy. From the chemical abundance determinations we demonstrate that PNe are enriched in O and Ne. The average O abundance in H ii regions is 12 + log O/H = 7.74 ± 0.09 and PNe show significantly higher oxygen abundance by 0.43 dex in average. Ne abundance are about three times larger in PNe than in H ii regions. This is a very important result showing that because of the low metallicity in the galaxy, O and Ne in PNe have been enriched by their progenitors in nucleosynthesis processes and brought to the surface during third dredge-up events. Our PN abundances are better reproduced by some nonstandard stellar evolution models for a metallicity of Z = 0.001, similar to the metallicity of H ii regions. Abundances in H ii regions show no metallicity gradient in this galaxy. We discuss a possible connection between the kinematics and chemistry.