Spain did, at least at first.
The US claimed what became the New Mexico territory during the Mexican-American War. It was primarily a linear western extension from Texas.
A case can be made as early as 1848, when a peace treaty with Mexico was signed giving the US huge pieces of territory claimed to be owned by Mexico. In this situation, both countries can be said to have had imperial ambitions. The territory claimed by Mexico was the land the Spanish previously "stole" from Native Americans.
The US claimed what became the New Mexico territory during the Mexican-American War. It was primarily a linear western extension from Texas.
Mexico claimed the Nueces River defined the US-Mexico border.
Which river did Mexico claim was the border between Texas and Mexico
The Oregon Country was explored and claimed by various nations in the early 19th century, while Texas declared independence from Mexico in 1836 and became a Republic. The land ceded by Mexico to the United States came after the Mexican-American War, formalized in the Treaty of Guadalupe Hidalgo in 1848. Therefore, the Oregon Country was claimed first, followed by Texas, and then the land ceded by Mexico.
Mexico claimed the Rio Grande River as their border.
Before the Mexican/American War, Mexico claimed it was the Nueces river, while Texans claimed it was the Rio Grande.
Nueces River and the the Rio Grande River. Mexico claimed that the Nueces river was the Texas and Mexico border. The US claimed that the Rio Grande was the correct location.
MEXICO owend it
Mexico