We present the results of a search for galaxy clusters in the first 36 XMM-Newton pointings on the COSMOS field. We reach a depth for a total cluster flux in the 0.5-2 keV band of 3x10-15 ergs cm-2 s-1, having one of the widest XMM-Newton contiguous raster surveys, covering an area of 2.1 square degrees. Cluster candidates are identified through a wavelet detection of extended X-ray emission. Verification of the cluster candidates is done based on a galaxy concentration analysis in redshift slices of thickness of 0.1-0.2 in redshift, using the multi-band photometric catalog of the COSMOS field and restricting the search to z<1.3 and i_AB < 25. We identify 72 clusters and derive their properties based on the X-ray cluster scaling relations. A statistical description of the survey in terms of the cumulative log(N>S)-lg(S) distribution compares well with previous results, although yielding a somewhat higher number of clusters at similar fluxes. The X-ray luminosity function of COSMOS clusters matches well the results of nearby surveys, providing a comparably tight constraint on the faint end slope of alpha=1.93+/-0.04. For the probed luminosity range of 8x10+42 - 2x10+44 ergs s-1, our survey is in agreement with and adds significantly to the existing data on the cluster luminosity function at high redshifts and implies no substantial evolution at these luminosities to z=1.3.
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