Federal contractors have started to build prototypes of the wall, which will be funded by the USA, despite Trump's pledges that Mexico would foot the bill.
The work on eight models is three months behind schedule in San Diego, AP reported. Construction of the wall prototypes is expected to last about a month.
"Today marks a significant milestone in the implementation of the President's executive order on border security and immigration improvement", said acting chief border patrol agent Roy Villareal during a press event at the construction site.
"It may not result in a singular victor". CBP could ultimately use all or none of the wall types along the border, Vitiello said, in addition to existing bollard fence designs that are used on the "immediate border".
As agents prepared for the news conference, a Mexican man breached the fence, cut his hand and was arrested.
New Trump Travel Ban Is Now Indefinite, Still Cruel and Xenophobic
The matter will be ultimately decided when the Supreme Court hears arguments on the merits of the executive order in October. Romero, the executive director of the American Civil Liberties Union, which has been challenging the ban in court.
"San Diego Patriots endorses the Fence/Wall and is happy to see the progress being made to secure our borders safely from foreign threats", said Amy Sutton, the leader of the San Diego Patriots.
San Diego police and the county sheriff's department have helped set up a "free speech zone" nearby for people to demonstrate. Villarreal said he knew of no organized plans to protest.
Mr Trump said on Friday that the wall should be see-through, repeating earlier claims that it should be transparent to curb the flow of drugs into the country. Another 300 miles have vehicle barriers, which allow easy penetration by pedestrians or animals but are created to stop trucks and cars from barreling over the border. It has issued two waivers since August, the first ones since 2008, on grounds of national security. In fact, the prototypes can be disassembled after construction. Recently, a leaked DHS report estimated that building 1,250 miles of fencing and wall could cost $21.6 billion. Four of them will be built of concrete, and the rest from alternative materials.
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