I don't believe that european settlers are directly responsible for millions of Native American deaths. In Canada the introduction of firearms made hunting so easy that some animals that were staple foods for natives nearly became extinct. These animals were nearly hunted to extinction by natives and european settlers alike, not for food, but for their pelts as well. It was just sheer greed, which led to a collapse of the native food supply and starvation. Millions of natives may have died of starvation long before their lands were ever encroached upon by significant numbers of settlers.

But we all know there were massacres of natives... Early records of genocides started with the Spanish conquistadors as soon as they landed. The genocide of Native North Americans may have started with the London Company in the 1600's as described here. Religious leaders set the tone for what occurred using shockingly familiar language:

"... in 1608 Sir Edward Coke, in his capacity as Lord Chief Justice offered a ruling in Calvin's Case which went beyond the issue at hand: whether a Scotsman could seek justice at an English Court. Coke distinguished between aliens from nations at war with England and friendly aliens, those from nations in league with England. Friendly aliens could have recourse to English courts. But he also ruled that "all infidels" (i.e. those from non-christian nations) there can be no peace and a state of perpetual hostility would exist between them and Christians. By so doing, Coke had created a warrant for genocide, in line with the intentions of the company. "

Separation of church and state came far too late in the west, and still hasn't been employed in some other parts of the world.