Russell Means, the Lakota activist and founder of the American Indian Movement (AIM), has strongly rejected Native American in favor of Indian:

I abhor the term Native American. It is a generic government term used to describe all the indigenous prisoners of the United States. These are the American Samoans, the Micronesians, the Aleuts, the original Hawaiians, and the erroneously termed Eskimos, who are actually Upiks and Inupiats. And, of course, the American Indian.

I prefer the term American Indian because I know its origins . . . As an added distinction the American Indian is the only ethnic group in the United States with the American before our ethnicity . . . We were enslaved as American Indians, we were colonized as American Indians, and we will gain our freedom as American Indians, and then we will call ourselves any damn thing we choose.

“I am an American Indian, Not a Native American!”
statement by Russell Means