New generalization of the z-scaling in inclusive particle production is proposed. The scaling variable z is expressed in terms of the momentum fractions x1 and x2 of the incoming protons. Explicit dependence of z on the momentum fractions y a and y b of the scattered and recoil constituents carried by the inclusive particle and recoil object is included. The scaling function psi (z) for charged and identified hadrons produced in proton-proton collisions is constructed. The scheme allows unique description of data on inclusive cross sections of charged hadrons, pions, kaons, antiprotons and lambdas produced at RHIC energies. The obtained results suggest that the z-scaling may be used as a tool for searching for new physics phenomena of particle production in high transverse momentum and high multiplicity region at proton-proton colliders RHIC and LHC.