The approximately 325 federal Indian reservations are formally and legally called "domestic dependent nations". So, you might consider this "their own countries".
As domestic dependent nations, Indian tribes exercise inherent sovereign powers over their members and territory.
The United States recognizes the right of Indian tribes to self-government and supports tribal sovereignty and self-determination.
NCSL (2013):
The U.S. Constitution recognizes Indian tribes as distinct governments and they have, with a few exceptions, the same powers as federal and state governments to regulate their internal affairs.
Tribes possess all the powers of self-government, including the rights to:
• Form a government
• Make and enforce laws, both civil and criminal
• Tax property or sales
• Establish and determine tribal membership
• License and regulate activities within their jurisdiction (including hunting, environmental control, land use, and gambling)
• Exclude people from tribal lands
Tribes cannot declare war, engage in foreign diplomacy, or print and issue their own currency.