The reaction came after the American Civil Liberties Union (ACLU) on Thursday reported on the operations of the United Constitutional Patriots (UCP), which patrols the southern US border in New Mexico.
In a statement, Mexico's Foreign Relations Ministry denounced "militia groups" operating "on the margins" of the law.
"These types of practices can drive human rights abuses of people who migrate or request asylum or refuge in the United States," it said.
The ACLU has described the vigilantees as a "fascist militia organization" supported by the US administration and called on US officials to investigate the “kidnapping” of hapless asylum seekers, Presstv reported.
The group has posted videos showing members dressed in camouflage and armed with semi-automatic rifles holding groups of refugees until US Border Patrol agents arrive.
"We urge you to immediately investigate this atrocious and unlawful conduct" and stop UCP's illegal activities, the ACLU said, making its plea to US state officials.
"We cannot allow racist and armed vigilantes to kidnap and detain people seeking asylum," it added.
The militia groups say they are helping the Border Patrol deal with a surge in refugees which US President Donald Trump has described as an "invasion" and some of them as "animals".
The Trump administration has also toughened various policies and put pressure on Mexico in an attempt to discourage people from attempting to cross into the United States.
New Mexico Democratic senators Martin Heinrich and Tom Udall called for an investigation into the militia groups in a joint statement on Friday.
“Reports of a militia group illegally operating in New Mexico and intimidating asylum seekers must be immediately investigated by the proper authorities. Vigilante groups attempting to utilize authorities reserved for law enforcement cannot be tolerated."
The US Federal Bureau of Investigation (FBI) said Saturday its agents had arrested a man who allegedly led the UCP.
It identified the man as 69-year-old Larry Mitchell Hopkins, also known as Johnny Horton Jr., a convicted felon and singer with a long criminal record. He was arrested for illegal possession of firearms.
“This is a dangerous felon who should not have weapons around children and families. … law should be in the hands of trained law enforcement officials, not armed vigilantes,” New Mexico’s Attorney General Hector Balderas said.
Hopkins has reportedly told local media he had a longstanding relationship with President Trump and had received his modus operandi from the highest level.
His militiamen have allegedly rounded up thousands of asylum seekers, mostly children, crossing the border into the US and helped spread and strengthen far-right ideas promoted by Trump.
Trump deployed about 5,800 troops to the Mexican border last November, some of whom were later withdrawn.
Acting US Defense Secretary Patrick Shanahan, however, said in January that the Pentagon was planning to send thousands more troops back to the US border with Mexico.