Raphael Lemkin, the man who coined the term "genocide", defined it this way:

Generally speaking, genocide does not necessarily mean the immediate destruction of a nation, except when accomplished by mass killings of all members of a nation. It is intended rather to signify a coordinated plan of different actions aiming at the destruction of essential foundations of the life of national groups, with the aim of annihilating the groups themselves. The objectives of such a plan would be the disintegration of the political and social institutions, of culture, language, national feelings, religion, and the economic existence of national groups, and the destruction of the personal security, liberty, health, dignity, and even the lives of the individuals belonging to such groups.

From this perspective, mass killings are an instrument of genocide, not the definition of it.

In any case, a case can be made that the treatment of native american groups by the US government qualifies. For the last several hundred years, one of the prevailing attitudes held by officials towards natives was the "kill the indian, save the man" ethos. In other words, initiatives focused on assimilating natives into mainstream US society, usually by abandoning previous cultural traditions. The Dawes Act of 1887, for example, granted the President the authority to divide reservation land into individually owned plots, trying to make native americans private citizens of contemporary US society rather than members of tribal organizations. For some groups, this disrupted traditions of communal living that had wide-ranging impacts on their way of life. This was one of a number of attempts to compel large, semi-sedentary native groups to become sedentary farmers and property owners.

Besides this, the Bureau of Indian Affairs regularly adopted policies to encourage the use of English and conversion to Christianity at the expense of indigenous traditions.