According to oral tradition passed from Aztecs to Spanish/early mestizo(Mexican) historians; the Aztecs where from a mythical land called "Aztlan" no one knows exactly where these "mythical" kingdom existed but historians speculate it could be southwestern region of the U.S. (Utah). I say mythical because no one can prove it beyond a reasonable doubt; but according to these "mythical" tales passed by surviving Nahuatl people's the Aztecs left Aztlan because their god Huitzilopochtil commanded them to erect a new city in his honor. He instructed the Aztecs to build this city where an eagle would devour a serpent over a cactus; but according to Aztec legend the Aztecs had their form of exodus where they spent approx 100-200(some claim longer) years living as nomads traveling looking for the sign Huitzilopochtil the god of war gave them. According to the Nahuatl survivors the Aztecs under this period were warring with tribes and even themthe Aztecs themselves became indentured servants to bigger and stronger tribes, but ultimately where able to win their freedom.
Here's the big If: if the Aztecs "homeland" was indeed by southwestern U.S then the tribes they were warring with would of been the Ancestors of some of the modern native Americans today. So the answer to your question is yes that it's very likely the the Aztecs fought "U.S native Americans". But ultimately we will never know unless an ancient text or artifact with concrete evidence connects the Aztecs to south western U.S. Unfortunately a lot of misinformation has spread through Chicano movements that have radicalized these "Aztec mythological" stories. If anyone truly wants to learn I encourage you all to travel and visit the the ruins in Mexico. Specifically the Pyramid of the sun(was not built by Aztecs but later inhabited by them)there you will find descendants of Nahuatl survivors who still speak Nahuatl and will tell you about other stories and Aztec mythology that's been passed down from generation to generation.
The reason I believe the Aztecs are originally from southwestern U.S is because they were so unlike natives that inhabited the valley of Mexico; it's also speculated that the Aztecs started off as hunters and gathers and didn't have the technology or knowledge to build pyramids, during their exodus they assimilated and adopted tradition of their new neighboring tribes such as practicing Culhuacan and Azcapotzalco rituals and incorporating the technology for building and growing food. So if the Aztecs indeed did fight "U.S Native American" than it was a very primitive aztec clan composed of nomadic hunter gathering that was very war like and brutal, but had limited resources and far from an empire.