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Our results for the nontrapping invasion percolation model indicate that the statistics of the mass of invaded clusters is significantly dependent on the local occupation probability (pressure) pe at the extraction site. For pe=0 , we show that the mass distribution of invaded clusters P(M) follows a power-law P(M)˜M-α for intermediate values of the mass M , with an exponent α=1.39±0.03 . When the local pressure is set to pe=pc , where pc corresponds to the site percolation threshold of the lattice topology, the distribution P(M) still displays a scaling region, but with an exponent α=1.02±0.03 . This last behavior is consistent with previous results for the cluster statistics in standard percolation. In spite of these differences, the results of our simulations indicate that the fractal dimension of the invaded cluster does not depend significantly on the local pressure pe and it is consistent with the fractal dimension values reported for standard invasion percolation. 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