What idea prompted the United States to try and claim New Mexico?

Before the American Civil War the idea of Manifest Destiny was used to validate continental acquisitions in the Oregon Country, Texas, New Mexico, and California. Later it was used to justify the purchase of Alaska and annexation of Hawaii.

Explanation:

he believed that strong monarchies would lead to social and political stability.

as general terms,  indian territory,  the indian territories, or  indian country  describe an evolving land area set aside by the  united states government  for the relocation of  native americans  who held  aboriginal title  to their land. in general, the tribes ceded land they occupied in exchange for  land grants  in 1803. the concept of an indian territory was an outcome of the 18th- and 19th-century policy of  indian removal. after the  civil war(1861–1865), the policy of the government was one of  assimilation.