Previous determinations of the oxygen isotopic ratios in AGB carbon stars were at odds with the existing theoretical predictions. We aim to redetermine the oxygen ratios in these stars using new spectral analysis tools and further develop discussions on the carbon and nitrogen isotopic ratios in order to elucidate this problem. Oxygen isotopic ratios were derived from spectra in the K-band in a sample of galactic AGB carbon stars of different spectral types and near solar metallicity. Synthetic spectra calculated in LTE with spherical carbon-rich atmosphere models and updated molecular line lists were used. The CNO isotope ratios derived in a homogeneous way, were compared with theoretical predictions for low-mass (1.5-3 M_o) AGB stars computed with the FUNS code assuming extra mixing both during the RGB and AGB phases. For most of the stars the 16O/17O/18O ratios derived are in good agreement with theoretical predictions confirming that, for AGB stars, are established using the values reached after the FDU according to the initial stellar mass. This fact, as far as the oxygen isotopic ratios are concerned, leaves little space for the operation of any extra mixing mechanism during the AGB phase. Nevertheless, for a few stars with large 16O/17O/18O, the operation of such a mechanism might be required, although their observed 12C/13C and 14N/15N ratios would be difficult to reconcile within this scenario. Furthermore, J-type stars tend to have lower 16O/17O ratios than the normal carbon stars, as already indicated in previous studies. Excluding these peculiar stars, AGB carbon stars occupy the same region as pre-solar type I oxide grains in a 17O/16O vs. 18O/16O diagram, showing little spread. This reinforces the idea that these grains were probably formed in low-mass stars during the previous O-rich phases.
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