ALBUQUERQUE — Congress has so far thwarted President Trump’s plan to build a wall along the border with Mexico. But that hasn’t stopped some supporters from finding a way to build their own barrier.

A group that pushes for stricter border control is spending $6 million to construct less than a mile of border fencing on private land in southern New Mexico. Their hope is for the project to help limit the flow of migrant families trying to enter the United States around El Paso.

“It really was ridiculous how easy it was to get around the El Paso wall until we built this,” said Kris Kobach, who is known for his hard-line stance on immigration and is on the advisory board of the group, We Build the Wall, which collects donations to finance a barrier on the southern border.

Mr. Kobach unveiled the fencing on Memorial Day on land in Sunland Park, N.M., owned by the American Eagle Brick Co. He said that the company hired to build the wall, Fisher Industries of North Dakota, hoped to complete the project in a few days.