The American Civil Liberties Union of New Mexico joined a nationwide protest by rallying near the Columbus Port of Entry and informing border crossers of their Constitutional rights.
Advocates say they want to prevent potential civil and human rights abuses.
Similar checkpoint protests were held in California, Arizona, and Texas.
Meanwhile, the mayor of a southeastern New Mexico city where some immigrants were being detained shot down rumors that an immigrant had escaped.
Artesia Mayor Phillip Burch said immigration officials accounted for the 200 or so immigrant women and children being housed at the city's Federal Law Enforcement Training Center.