Monty Ray Turner, who is 51, agreed to remain in custody at a detention review hearing.
The Canada Border Services Agency is still preparing evidence for an admissibility hearing, which could be held as early as Friday.
At that hearing, the agency will seek to have Turner sent back to the United States because he faces serious criminal charges there.
Turner is suspected of breaking into his estranged wife's home last month, attacking her with a stun gun and pepper spray, and kidnapping the couple's three-year-old son, Luke.
Turner and his son were discovered the next day at a motel in Brandon, Man., and it remains unclear how they got across the border.