In the same press conference, Trump also made said his administration is finalising plans that would include potentially denying asylum claims if migrants and refugees cross in between ports of entry.
Mr Trump has unveiled his immigration policy ahead of the midterm elections on 6 November.
"We're going to hold them right there", he said.
The caravan, once estimated at more than 7,000 people, is now down to about 3,500 asylum-seekers and other migrants and is still hundreds of miles from the border. But there now is not enough detention space to hold families who are coming across the border.
The military is working to create space, but nothing has been finalised.
And laws prevent children from being detained beyond 20 days.
President Donald Trump ordered troops to the border in response to a caravan of migrants slowly making its way through Mexico toward the United States and still about 900 miles away, with many dropping out.
But immigrant advocates at the border earlier this year said that Customs and Border Patrol officers made it hard for migrants to cross bridges, turning them away at the midpoint between Mexico and the US.
The only violence Trump has cited in justifying the militarization of the border is what he alleges took place along Mexico's border with Guatemala when the caravan of migrants confronted Mexican federal police at that border.
Amazon’s early Black Friday sale is now live!
And thanks to Target , all that holiday gift-giving is about to get even easier. I don't know about you, but this has to be my favorite part.
He also said yesterday that his administration was finalising a plan to block migrants who do not come into the United States at a legal port of entry from applying for asylum, although federal law allows any migrant in the United States to do so.
Under U.S. law, any foreign national who is in the U.S. or who arrives in the U.S.
The U.S. president has spent the final days of the campaign hammering the issue as he tries to energize Republican voters, and his favorite target has been the migrant caravan of nearly 4,000 people that is still more than 800 miles away from the nearest U.S. border.
Illegal crossings at the U.S. southern border have spiked recently, with border patrol agents picking up almost 2,000 people a day trying to enter from Mexico. "And so we are making that our soldiers, our Marines are going to be fully trained in how to do that interaction", Gen. Terrence O'Shaughnessy said.
The troops deployed as part of Operation Faithful Patriot are advancing the Customs and Border Protection mission by providing planning, engineering, transportation, logistics, and medical support.
The captioned reads: "Illegal immigrant, Luis Bracamontes, killed our people!"
The video is reminiscent of the infamous 1988 "Willie Horton" ad used against Democratic presidential candidate Michael Dukakis and condemned as racist.
Trump said atop the ad, "It is outrageous what the Democrats are doing to our Country".
Trump says the move would be aimed at preventing the entry of a caravan of migrants traveling from Central America.
Last week officials indicated 800 to 1,000 troops might be sent.
Gov. Miguel Angel Yunes announced Friday evening that authorities in Veracruz would be providing not only humanitarian assistance to the migrants but buses to leapfrog them to Mexico City after three grueling weeks spent walking along highways and hitching rides to reach the coastal state. Even Fox News, which serves as a bullhorn for the President's thinly-disguised racist broadsides, carried an op-ed saying "Trump should fix our immigration system - Not spread fear of immigrants".