A reproducible instability, which appears similar to those reported previously, has been observed and studied in a low-pressure 13.56 MHz inductively coupled gaseous electronics conference rf cell operating in oxygen. The instability has been observed in the form of periodic modulations in the light output, floating potential, electron and positive and negative ion densities. The magnitude and frequency of the modulations is sensitive to the plasma operating conditions and the modulation amplitude has been observed to be as high as 40%. The instability is observed in a pressure and power regime where both the capacitive and inductive modes can exist. The frequency of the oscillations increases with increase in gas pressure from 3 to 21 kHz. This pressure window coincides with the pressure regime where there exists a significant fraction of negative ions in both modes. Time-resolved measurements of the electron energy distribution functions and charged particle densities indicate that at all phases of the instability, the plasma parameters remain close to those of the inductive mode. A global model has been modified for an oxygen discharge and this provides a qualitative description of the instability. The global model predicts a smaller power and pressure window for the instability but it can provide a framework for the discussion of instabilities in weakly electronegative discharges.