A high-finesse optical cavity was employed to perform highly sensitive spectroscopy of molecular oxygen at wavelengths near 763 nm. An equivalent absorption length of ∼1 km was obtained by a 26-cm-long optical cavity with a finesse of 6000. An extended cavity diode laser was frequency locked to the cavity, and pure absorption profiles were recovered by monitoring of the cavity transmission during continuous scans of the cavity resonance through O2 rotational lines, allowing a detailed investigation of the line shapes. Phase modulation of the laser at a frequency equal to the cavity free-spectral-range frequency was employed for detection of weak absorption signals inside the cavity. A minimum detectable absorption coefficient of 6.9×10−11 cm−1 Hz−1/2 was measured. Finally, a test of the symmetrization postulate in 16O nuclei was demonstrated.