The FBI arrested Aron Rosner of Brooklyn this week on charges accusing him of providing financial assistance to members of the religious group Lev Tahor in an international abduction scheme. Critics call the group a "cult".
Mr Rosner's defence attorney did not respond to an email seeking comment on Thursday.
The FBI said in court filings that the children – 14-year-old Yante Teller and her 12-year-old brother Chaim Teller – were kidnapped on 8 December from their home in upstate New York and taken out of the country.
Surveillance footage shows the children walking out of the residence before 3am and entering a vehicle.
The boy was spotted with Lev Tahor members at a hotel in Mexico City days after the kidnapping, according to the court filings. The whereabouts of the children was not clear on Thursday.
The FBI did not respond to an email seeking comment.
The bureau said in the court filings that the children's mother had been a “voluntary member” of Lev Tahor, but escaped the group in recent weeks after the organisation became increasingly extreme.
Her father, Shlomo Helbrans, founded the sect and, in 1994, was convicted of kidnapping a 13-year-old in New York. Mr Helbrans was later deported to Israel.
“The mother indicated that it was not safe to keep her children there,” FBI Agent Jonathan Lane wrote in a criminal complaint filed in US District Court, referring to the group in Guatemala.
Mr Lane referred in the complaint to news accounts of Lev Tahor subjecting children to “physical, sexual and emotional abuse.”
The FBI said Mr Rosner transferred money on seven occasions that assisted members of Lev Tahor in the kidnapping.
He also is accused of speaking with several “co-conspirators about hotels in Mexico as well as purchases of flights, bus tickets, credit cards and food,” according to the criminal complaint.
Mr Rosner was ordered held without bail on Monday pending trial.
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