The answer is yes. Many roundups of this year’s scientific developments have highlighted the discovery that, as Science News. puts it, “people of European and Asian descent really have inherited a small percentage of their DNA from” Neanderthals. More recently a second ‘extinct’ group, the Denisovans, has been identified as the partial ancestors of Melanesians. Many of these stories refer to Neanderthals and Denisovans as separate species from Homo sapiens. National Geographic’s headline, for example, reads “Neanderthals, Humans Interbred,” and the Los Angeles Times refers to the Denisovans as “a previously unknown hominid species.” Since no universally applicable definition of species exists, I guess that we can call anything a separate species. But, by biologists’ most common definitions, we, our Homo sapien ancestors, Neanderthals, and Denisovans are all part of the same species.
A common standard for considering whether individual organisms are part of the same species is whether they can breed with each other to produce breeding offspring. Since this is the crux of the new discoveries, clearly Homo sapiens, Neanderthals, and Denisovans meet this criterion.
Here’s another way to approach this issue: the vast majority of members of all human groups today can interbreed with members of other groups: Melanesians with Europeans with Africans. And all humans today are very similar genetically. Thus they are part of the same species. Phylogenetically, it makes little sense to state that Europeans and Asians are 1-4% from another species; this would result in an unusual phylogenetic chart (aka family tree). It makes much more sense to state that anyone descended from the common ancestor of Neanderthals, Denisovans, and ancient Homo sapiens is part of the same species.
This means that our species was much more diverse in the past than had been thought and that it is older by several hundred thousand years.
If we call our species Homo sapiens, then Neanderthals and Denisovans were Homo sapiens, too. We thus might want a different name for the Homo sapiens who remained in Africa after the group that became the Neanderthals migrated away. “Modern humans” was never a good term and is now much worse, especially when it is used in contrast with Neanderthals.
Finally, a note about terminology: Many researchers, when being careful, refer to all of these groups and others, such as Homo erectus and Homo ergaster, as “humans.” For example, the Smithsonian Institution says, “There were many times in the past when several early human species lived at the same time.”