Building a border wall remains a signature campaign issue for Trump, who claimed at a rally in Arizona this week that under his administration the southern border was the "most secure" in US history.
"We built almost 400 miles," Trump said Wednesday, referring to the wall. The administration is trying to reach 450 miles by year's end.
Wolf didn't specify the exact number of miles that had been constructed Thursday, saying only that it was "nearly 400." While most of the new wall construction has replaced barriers already along the southwest border, the new construction is taller (18 to 30 feet) and in many cases bolstered by surveillance systems and access points.