Native American Veterans' Memorial Amendments Act of 2013 - Amends the Native American Veterans' Memorial Establishment Act of 1994 to authorize the construction of the National Native American Veterans' Memorial on the property of the National Museum of the American Indian. (Currently, its location is restricted to the interior structure of the Museum.)

Authorizes the Museum to participate in the selection of the Memorial's design, on more than a consultative basis, with the National Congress of American Indians.

Makes the Museum and the National Congress of American Indians responsible for accepting contributions for, and paying the expenses of, establishing the Memorial. (Currently, the National Congress of American Indians is solely responsible for those duties.)