Some 2,100 National Guard reservists have already been active in the area for several months, so the arrival of the latest troops will bring the total United States military presence to 9,000.
"I noticed all that lovely barbed wire going up today", Trump said at a Montana campaign rally on Sunday.
The Patriots of the Constitution militia put out a call last month for a "full deployment" to make a "stand to secure our border from a mob of migrating immigrants", the Albuquerque Journal reported.
"Members who are deployed in support of the Department of Homeland Security's border mission are not eligible for imminent-danger pay", he said in a statement Monday.
The Trump administration discussed using the us military to build facilities to house detained migrants as part of its new mission on the Mexican border but the idea was dropped after the Pentagon expressed doubts about it, USA officials said. "We are providing enabling capabilities".
By voicing its opposition, the Pentagon helped ensure that its mission was tailored to only providing support to USA government personnel on the border, US officials said. Troops will also be providing medical support. "But we're going to arrest those people quickly and for a long time".
Bush ordered Operation Jump Start, which lasted from 2006 to 2008, and deployed 6,000 National Guard troops to California, Arizona, New Mexico and Texas.
That's why it's so striking that Trump continues to say the military will take actions it likely won't.
Highlighting the limited scope of the military's involvement in the large-scale effort to plug the gaps in the porous border, Pentagon spokesman Col. Rob Manning said that of all the troops only Military Police servicemen will carry arms. One official says that DHS was informally discouraged from making the request by the defense department. He denied widespread media reports that the military should engage in the construction of accommodation facilities for migrant families.
Trump said last week he plans to build tents to house migrants, who would be held in those facilities while the USA government weighs their asylum request.
Reuters was first to report that the Pentagon had balked at the initial request from the Department of Homeland Security.
Asked about the cost of the operation, Manning said it had yet to be determined by the Pentagon's financial services.