The US? I'm pretty sure it was the British, Spanish, and other European colonizers who killed off most indigenous New World inhabitants long before the USA even existed. And although that genocide involved a significant amount of violence (some perpetrated by the US government in the later stages), most of the deaths were caused by the inadvertent spread of infectious diseases.
I suspect you may have an overly sanitized view of the US impact on indigenous populations, at least in North America. You might want to read about the "Indian Wars" post US revolution and efforts by the US government such as those to eradicate bison as a means to wipe out the Plains Indian tribes, the Trail of Tears, the California Genocide, etc., etc.
Not at all. I am fully aware of the terrible, genocidal crimes that the US government (or private US citizens under government protection) committed against indigenous populations. And I make no excuses for those. But if you look at the numbers, Europeans caused a lot more total deaths in the Americas.
Is there actually a difference? The people you call Americans and the people you call Europeans are the same people (in this time period). It doesn't matter if they changed the design on their flags before they charged into certain battles.
Assign the labels or draw the lines however you like. It doesn't change the main point. I was responding to @holyra above who claimed that the USA has a "violent culture", but there is no historical evidence to support such a claim. Over any lengthy period you look at the USA has on average been no more violent (and generally less so) than most European countries. I just find it funny when Europeans who are ignorant of their own history and traditional proclivities try to claim some sort of cultural superiority.
Even in the US, we cover this very explicitly in our history courses. Europeans did displace and kill a lot of natives, but it was the US that almost genocided them long after colonization was over.
See: the Trail of Tears, the actual, literal death march of natives out of their ancestrial lands because "manifest destiny"