A comparison of the complete genome of three sets of Neanderthal remains from Croatia from 40,000 years ago, with a small number of widely geographically dispersed modern humans suggests that 1%-4% of modern non-African DNA has a Neanderthal source. The most plausible source of these genes is interbreeding between the pre-dispersal Out of Africa population and Neanderthals.
This is in addition to any common ancestry from Neanderthals shared by all African and non-African modern humans due to back migration of Neanderthals from the Near East and Europe to Africa. Neanderthal expert and anthropology blogger John Hawks also suggests that the research design wouldn't show genetic contributions from non-Neanderthal hominins other than Neanderthals that early modern humans might have encountered outside Africa.
Our limited knowledge of the population sizes of the Neanderthal and early modern human populations, and about the selective benefits of Neanderthal genes that remain make it hard to determine just how high the rate of interbreeding was in early human populations.
Earlier studies of much smaller portions of Neanderthal and modern human DNA had suggested a high likelihood that there was no Neanderthal DNA legacy in modern humans.