It was not immediately clear how long the construction pause would last.
Federal agents were attempting to apprehend the 34-year-old man near Arivaca, Arizona, when he shot at a Border Patrol helicopter and at agents, the FBI said.
The Trump administration is adding another militarized zone to the southern U.S. border to support border security operations - this time in California.
A federal judge said Wednesday that an order by President Donald Trump suspending asylum access at the southern border was unlawful, throwing into doubt one of the key pillars of the president's plan to crack down on migration at the southern border.
The streets of El Paso today are vastly different than a year or two ago when hundreds of migrants with hope of a life in the United States made the border city their transitionary point.