Context.The presence of magnetic fields in O-type stars has been suspected for a long time. The discovery of these fields would explain a wide range of well documented enigmatic phenomena in massive stars, in particular cyclical wind variability, Hα emission variations, chemical peculiarity, narrow X-ray emission lines, and non-thermal radio/X-ray emission. Aims.To investigate the incidence of magnetic fields in O stars, we acquired 38 new spectropolarimetric observations with FORS 1 (FOcal Reducer low dispersion Spectrograph) mounted on the 8-m Kueyen telescope of the VLT. Methods.Spectropolarimetric observations were obtained at different phases for a sample of 13 O stars. Ten stars were observed in the spectral range 348−589 nm, HD 36879 and HD 148937 were observed in the spectral region 325−621 nm, and HD 155806 was observed in both settings. To prove the feasibility of the FORS 1 spectropolarimetric mode for the measurements of magnetic fields in hot stars, we present in addition 12 FORS 1 observations of the mean longitudinal magnetic field in θ1 Ori C and compare them with measurements obtained with the MuSiCoS, ESPaDOnS, and Narval spectropolarimeters. Results.Most stars in our sample, which were observed on different nights, show a change of the magnetic field polarity, but a field at a significance level of 3σ was detected in only four stars, HD 36879, HD 148937, HD 152408, and HD 164794. The largest longitudinal magnetic field, Bz = −276 ± 88 G, was detected in the Of?p star HD 148937. We conclude that large-scale organized magnetic fields with polar field strengths larger than 1 kG are not widespread among O-type stars.