The number of troops would include the initial wave of 5,239 active duty troops, 2,100 National Guard forces already there, and another 2,000 to 3,000 on prepare-to-deploy orders.
The US has 5,262 troops now on deployment in Iraq and around 2,000 in Syria.
About 1,000 active-duty troops had already arrived in Texas on Tuesday, where O'Shaughnessy said they would begin their mission of tightening up the border before moving on to other areas in Arizona and California.
Senior military officers have defended the deployment on national security grounds. Mexican officials said the migrants were wanted for drug trafficking and murder, respectively, in their native Honduras.
But Trump has painted a different picture with his rhetoric, casting the deployment as a necessary intervention to stop potentially unsafe individuals from entering the country.
The officials emphasized the troops will be at the border to support civil authorities and that they are not expected to come into any contact with migrants.
"Our military is being mobilised at the Southern Border", Trump tweeted.
Still, sending this many troops to the border seems to compound a vision of this caravan as an "invading force" that requires a sizable border force to repel. We do this following storms, we do this in support of the Department of Homeland Security.
On Tuesday they covered about 25km and settled down for the night in the town of Tapachula in the state of Chiapas, an AFP reporter said.
President Donald Trump's complaints that Mexico is not doing enough to stop a caravan of migrants are being contradicted by his own White House. Almost two weeks ago, the caravan stormed through Mexico by tearing down the country's border fence with Guatemala.
Meanwhile, Trump has also vowed that the illegal migrants won't be allowed to cross into the U.S.
Asked if his decision to send troops was an attempt at fear-mongering in the days before next week's midterm elections, Trump blamed the lack of immigration reform on Democrats.
Defense Secretary Jim Mattis speaks at the Pentagon in Washington, Sept. 21, 2018.
However, a previous deployment of 6,000 troops from 2006 to 2008 cost $1.2 billion, the U.S. Government Accountability Office has reported.
"It's not about the footprint". The president said Thursday he will send up to 15,000 troops to the border to discourage the migrants.
As 700 Salvadoran migrants started their 1,500-mile journey by foot from the capital of El Salvador to the U.S. border Wednesday, in Washington, DC, the White House was vowing to deploy thousands of troops to stop them and thousands of other migrants from entering the United States.
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