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5 year oldLarry Mitchell Hopkins, 69, and his group United Constitutional Patriots, also plotted to target Hillary Clinton and billionaire George Soros, according to a tip received by the FBI.
It is unclear when he allegedly made these comments, which were included in court papers released this week.
His lawyer has denied the allegations.
"He says that is categorically false that that's what they were doing," Kelly O'Connell told NBC News. "There was no plan to do any of that."
Mr Hopkins appeared in court in Las Cruces, New Mexico, on Monday, charged with being a convicted criminal in possession of a firearm and ammunition.
He was arrested on Saturday, just days after the group hit the headlines for detaining migrants in the desert near the US-Mexico border.
The small volunteer group argues it is helping US Border Patrol to deal with a surge in migrants crossing America's southern border, but their actions - caught on camera - earned widespread condemnation from civil rights groups and local officials.
The FBI were apparently first made aware of the group United Constitutional Patriots in 2017.
According to an affidavit by Special Agent David Gabriel, the FBI received information in 2017 that the Patriots, based out of Mr Hopkins' residence, had about 20 members and was armed with AK-47 rifles, among other firearms.
"Hopkins also allegedly made the statement that the United Constitutional Patriots were training to assassinate George Soros, Hillary Clinton and Barack Obama, because of these individuals' support of Antifa [a left-wing group]," Mr Gabriel said.
But Mr O'Connell questioned why it had taken some two years to charge his client. He pointed out that the FBI had searched Mr Hopkins' residence in 2017, and discovered weapons that Mr Hopkins said were owned by his wife, but did not arrest him at that point.
"If it was that outrageous of a crime, why not lock him up right then?" he said.
Mr Hopkins now faces up to 10 years in prison, probation and $250,000 (£192,000) in fines, according to the Las Cruces Sun-News.
Under US law, convicted felons are generally prohibited from possessing firearms, and the FBI states Mr Hopkins has "at least one prior felony conviction".
In 1996, Mr Hopkins pleaded guilty to possessing a loaded firearm. In 2006, he was convicted of possessing a weapon and impersonating a police officer in Oregon.
A detention hearing has been scheduled for next week, and Mr Hopkins remains in custody until then.
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