Martinelli, 66, was suffering from heart problems, said Angel Cedeno, director of the Santo Tomas public hospital in Panama City.
Nauert said that Martinelli's extradition followed normal procedures established by the countries' bilateral extradition treaty.
Mr Martinelli is being sent to the same prison where Panama's former military leader, General Manuel Noriega, spent the last years of his life. He claims the charges are false claims from political enemies.
These targets included Martinelli's political allies and opponents, their family members, his business rivals, Panamanian judges, journalists, union activists, U.S. diplomats, and others.
U.S. Deputy Secretary of State John J. Sullivan issued a warrant ordering the ex-president to surrender to Panamanian authorities.
Martinelli's attorney said Friday she was informed a day earlier about the State Department's decision. On May 15 he asked the State Department to deny the extradition request, saying that he would be tortured in Panama.
USA authorities on Monday extradited Panama's ex-president Ricardo Martinelli, placing him on a private flight from Miami, Florida to Panama City. He is believed to have conducted most of the alleged illegal activity through an extensive surveillance system called the National Security Council, which carried out confidential activities at the direction of Martinelli. That agency used multimillion-dollar surveillance systems to listen in on and record cell phone conversations and computer communications from "targets", including Panamanian judges, US diplomats, union activists, political allies and opponents, relatives of politicians and business rivals, according to information in filings to support his extradition.