Meteorites contain relict decay products of short-lived radionuclides that were present in the protoplanetary disk when asteroids and planets formed. Several studies reported a high abundance of 60Fe (t1/2=2.62+/-0.04 Myr) in chondrites (60Fe/56Fe~6*10-7), suggesting that planetary materials incorporated fresh products of stellar nucleosynthesis ejected by one or several massive stars that exploded in the vicinity of the newborn Sun. We measured 58Fe/54Fe and 60Ni/58Ni isotope ratios in whole rocks and constituents of differentiated achondrites (ureilites, aubrites, HEDs, and angrites), unequilibrated ordinary chondrites Semarkona (LL3.0) and NWA 5717 (ungrouped petrologic type 3.05), metal-rich carbonaceous chondrite Gujba (CBa), and several other meteorites (CV, EL H, LL chondrites; IIIAB, IVA, IVB iron meteorites). We derive from these measurements a much lower initial 60Fe/56Fe ratio of (11.5+/-2.6)*10-9 and conclude that 60Fe was homogeneously distributed among planetary bodies. This low ratio is consistent with derivation of 60Fe from galactic background (60Fe/56Fe=2.8*10-7 in the interstellar medium from gamma-ray observations) and can be reconciled with high 26Al/27Al=5*10-5 in chondrites if solar material was contaminated through winds by outer layers of one or several massive stars (e.g., a Wolf-Rayet star) rich in 26Al and poor in 60Fe. We present the first chronological application of the 60Fe-60Ni decay system to establish the time of core formation on Vesta at 3.7 (+2.5/-1.7) Myr after condensation of calcium-aluminum-rich inclusions (CAIs).