The 12-person panel deliberated for about five hours Tuesday but left without deciding the fate of 77-year-old Hafiz Khan. They will resume discussions Wednesday.
Khan is accused of funneling about $50,000 to the Pakistani Taliban, which has been linked to numerous violent attacks including the 2010 attempt to bomb New York's Times Square.
Kahn testified that the money was for family, for charity, and for a religious school he owns in Pakistan's Swat Valley. He denied supporting the Taliban.
If convicted, Khan faces up to 15 years in prison on each of four terrorism support-related charges.