The two-, three- and four-body interaction energies in face-centered cubic (fcc) krypton are evaluated using the many-body expansion method and the coupled cluster theory with full single and double excitations plus perturbative treatment of triples, and both self-consistent-field (SCF) Hartree-Fock energy and correlation one are accurately determined in a wide volume range (from 27 to 4 cm3/mol). All different three- and four-atom clusters existing in the first three and two nearest and two neighbor shells of fcc lattice are considered. It is found that the three-body interaction energy is positive at low compression, where the dispersive forces play a dominant role, with increasing the compression the three-body contribution becomes attractive, and the SCF energy overwhelms the dispersive one. At pressures higher than 30 GPa, the four-body contribution becomes important and significantly cancels the over-softening effects of the three-body potential. It shows that the combination of the four-body effects with two- and three-body interactions leads to an excellent agreement with the measurements from the equation of state in the whole experimental range of 0-130 GPa.