American Indian Movement founder Russell Means also began notifying foreign embassies worldwide, and plans to deliver the declaration to the United Nations.
"We are now a free country and independent of the United States of America," Means told the Rapid City (S.D.) Journal. "This is all completely legal."
The State Department has not responded, he told the newspaper.
The server for the Lakota Web site crashed Thursday after news spread of the Native American secession attempt.
Lakota tribes have contested the U.S. government over land they claim was promised by treaty then taken from them, particularly in western South Dakota. The tribes have refused a 1980 federal court settlement that awarded cash compensation but not land. That settlement is now valued at $1 billion, the Journal said.