The CBP statement said the vehicle stopped just a few yards into Mexico.
The CBP response came quickly after the Nogales City Council passed a resolution condemning the use of new razor wire that now covers the entirety of a tall border wall through downtown.
He is also giving an ultimatum to the federal government - remove the wire or there will be lawsuit, The Associated Press reports.
Migrants told authorities that buses and trucks dropped them off throughout the night on a nearby Mexican highway that runs parallel to the border and they entered the US together to wait for agents to find them.
So far this year, Customs and Border Protection says agents have apprehended three groups totaling more than 650 people in that part of the desert, between Yuma and Nogales.
Numerous migrants who may seek passage with smugglers in their journey through Mexico cross the border and turn themselves into USA authorities to seek asylum in the United States, a drawn-out court process that can take months or years to resolve.
USA authorities arrested or stopped people for immigration violations 58,207 times in January, down 4 percent from 60,779 in December but up 62 percent from 35,905 in January 2018.
Authorities closed the DeConcini Port of Entry near Nogales after a man was shot attempting to run over a border patrol agent on Thursday night.
CBP said it would release more information later Friday, but additional details had not been released by mid-afternoon. Illegal crossings in that area have dropped steeply in recent years.