Avoiding the rhetoric from President Donald Trump that troops were sent in response to an "invasion" by a massive caravan of migrants seeking entry into the United States, O'Shaughnessy said Operation Faithful Patriot is meant to "secure the border".
His warning comes as the United States military is reportedly preparing to send 5,000 troops to the border, a significant increase over the initial estimates of 800 reported last week.
The caravan, which has included as many as 7,200 people and is now approximately 1,000 miles from the closest border crossing with the US, has become a major issue with less than two weeks before the November 6 midterm elections.
Trump railed against illegal immigration to win the 2016 presidential election and has seized on the caravan of Central American migrants at campaign rallies in the run-up to next week's vote. Thousands have already dropped out, applying for refugee status in Mexico or taking the Mexican government up on free bus rides back home, and the group is likely to dwindle even more during the arduous journey ahead.
O'Shaughnessy said that the U.S.is "working closely to understand the nature and makeup of this caravan".
Mexico's Interior Ministry said that temporary identity numbers have been issued to 111 migrants, which would allow the migrants to stay and work in Mexico.
About 2,100 have deployed.
Luis Acosta holds 5-year-old Angel Jesus, both from Honduras, as a caravan of migrants from Central America en route to the United States crossed through the Suchiate River into Mexico from Guatemala in Ciudad Hidalgo, Mexico on October 29, 2018. "To use active-duty military and put them in that role, I think is a huge mistake".
Other agencies have periodically tried to impede or erode the mass migration, whose progress has led President Trump to threaten action against Mexico. The trip could be twice as long if the 4,000 or so migrants head for the Tijuana-San Diego frontier, as another caravan did earlier this year.
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"There are people fainting, there are wounded", said Martin Rojas, an agent of Grupo Beta who spoke to The Associated Press after dropping off a group of women and children in Tapanatepec after spotting them on a highway trudging through temperatures approaching 104 degrees Fahrenheit (40 degrees Celsius).
"The 5,239 are going forward and there will be additional forces over and above the 5,239", he said, adding that number "is not the top line".
O'Shaughnessy said some soldiers would be armed although it was unclear who, beyond US military police, might need those weapons.
It's unclear if the caravan, which is reportedly moving about 25 miles each day, could arrive at the border in that time. Only about 200 in that group made it to the border.
Under the Posse Comitatus Act, federal troops are mostly prohibited from engaging in domestic law enforcement activities.
That's in addition to the more than 2,000 members of the National Guard already helping at the border now.
On Sunday, Mr Mattis told reporters that some construction materials were already being moved to the border, including barriers.
Brown said the California troops would help fight transnational criminal gangs and drug and firearms smugglers.
The standoff on the riverbank follow a more violent confrontation that occurred on the nearby bridge over the river the night before, when migrants tossed rocks and used sticks against Mexico police.