We report on a search for inclusive production of squarks and gluinos in pp collisions at s√=1.96  TeV, in events with large missing transverse energy and multiple jets of hadrons in the final state. The study uses a CDF Run II data sample corresponding to 2  fb−1 of integrated luminosity. The data are in good agreement with the standard model predictions, giving no evidence for any squark or gluino component. In an R-parity conserving minimal supergravity scenario with A0=0, μ<0, and tanβ=5, 95% C.L. upper limits on the production cross sections in the range between 0.1 and 1 pb are obtained, depending on the squark and gluino masses considered. For gluino masses below 280  GeV/c2, arbitrarily large squark masses are excluded at the 95% C.L., while for mass degenerate gluinos and squarks, masses below 392  GeV/c2 are excluded at the 95% C.L.