(In an earlier message) I informed you that ... I had ordered an efficient military force to take a position "between the Nueces and the Del Norte (Rio Grande)." This had become necessary, to meet a threatened invasion of Texas by the Mexican forces ... The invasion was threatened solely because Texas had determined ... to annex herself to our Union; and, under these circumstances, it was plainly our duty to extend our protection over her citizens and soil.

... The Congress of Texas, by its act of December 19, 1836, had declared the Rio del Norte to be the boundary of that republic.... The country between that river and the Del Norte ... is now included within one of our congressional districts.... It became, therefore, of urgent necessity to provide for the defense of that portion of our country....
(On the 24th of April) a party ... of sixty-three men and officers, were ... dispatched from the American camp up the Rio del Norte, on its (North) bank, to ascertain whether the Mexican troops had crosses, or were preparing to cross, the river.... (They) became engaged with a large body of these (Mexican) troops, and, after a short affair, in which some sixteen (Americans) were killed and wounded, appear to have been surrounded and compelled to surrender....
We have tried every effort at reconciliation. The cup of forbearance had been exhausted even before the recent information from the frontier of the Del Norte. But now, ... Mexico has passed the boundary of the United States, has invaded our territory and shed American blood upon the American soil.

Would Mexico have viewed a Mexican advance north of the Rio Grande an invasion of the US?

To determine Mexico's perspective on whether their advance north of the Rio Grande would be seen as an invasion of the United States, we can analyze the historical context and the actions taken by both countries. In the message provided, it is evident that the United States believed Mexico's advance across the Rio Grande as an invasion. However, to get a complete understanding, we can examine additional historical records and perspectives from Mexico during that time.

1. Research Mexican claims and actions: Study official Mexican documents, government proclamations, diplomatic correspondences, and historical accounts from that era. This can help in understanding Mexico's position on the territory between the Nueces and the Rio Grande.

2. Explore Mexican public sentiment: Look for public speeches, newspaper articles, and other sources of Mexican public opinion regarding the disputed territory and their intentions towards it. This can provide insights into how Mexico and its citizens perceived the situation.

3. Analyze diplomatic interactions: Review diplomatic exchanges between Mexico and the United States during that period. Pay close attention to negotiations, treaties, and any agreements made between the two countries regarding their respective territories.

4. Evaluate Mexican military movements and intentions: Examine military actions taken by Mexico in the region. Look for evidence of military preparations, troop movements, or any other indicators that could shed light on Mexico's intentions and whether they considered it an invasion of the United States.

By conducting thorough research and analysis using historical records and perspectives from both countries, you can gain a more comprehensive understanding of how Mexico would have viewed their advance north of the Rio Grande in relation to a potential invasion of the United States.