(CNN) -- The United States has brought Abu Anas al Libi -- an alleged al Qaeda operative whom U.S. Army Delta Force soldiers captured in Libya this month -- to New York, a U.S. attorney's office said Monday.
He was transferred to law enforcement custody and brought to the United States on Saturday, according to a letter from the office of Manhattan U.S. Attorney Preet Bharara to a federal judge.
Al Libi is expected to appear before a judicial officer on Tuesday, Bharara's office said.
His family in Tripoli said they were shocked that he was in the United States. They had received no details of his whereabouts from the U.S. or Libyan governments, family members told CNN.
His son, Abdullah, said the family hoped to get him a lawyer that would "work with him, for him." It was unclear if al Libi already has a lawyer.
"We don't want him talking to just anyone," Abdullah said. "We don't want just any lawyer asking him questions."
A U.S. official said al Libi received care at a medical facility in New York for a pre-existing medical condition and is "doing better."
The official did not detail the medical issue. His wife told CNN this month that al Libi has a severe case of hepatitis C and that she was worried about his health.
U.S. special operations forces captured al Libi in Tripoli more than a week ago. The 49-year-old native of Libya is accused of playing a role in the 1998 U.S. Embassy bombings in Kenya and Tanzania.
The United States had been holding him aboard a Navy ship, U.S. officials said. He was questioned there by members of a high-value detainee interrogation team, the officials said.
American officials have described him as "one of the world's most wanted terrorists."
He was indicted in 2001 by the federal court in the Southern District of New York in the embassy bombings and in connection with his alleged roles in al Qaeda conspiracies to attack U.S. forces in Saudi Arabia, Yemen and Somalia.
Some terrorism experts have questioned how much valuable intelligence al Libi would be able to provide for his captors. A former jihadist associate told CNN last week that it was unlikely that he was still playing an active role with the terrorist network.
His wife said he was no longer a member of al Qaeda, had been living a normal life and was seeking a job with the Libyan oil ministry.
Al Libi was captured October 5 on the street in front of his home as he returned in his car from morning prayers.
President Barack Obama and Attorney General Eric Holder have previously said they prefer to try individuals such as al Libi in American courts.
Trying such suspects on American soil has been a controversial topic in the past.
In 2009, Holder said five detainees with alleged ties to the September 11, 2001, attacks would be transferred from Guantanamo Bay, Cuba, to New York for trial in civilian court. Later Holder reversed course, announcing that accused 9/11 mastermind Khalid Sheikh Mohammed and others would be tried in a military commission at Guantanamo instead.
State Department deputy spokeswoman Marie Harf said last week that there was no chance that al Libi would end up at Guantanamo.
"The administration's position on Guantanamo is clear. Our goal is not to add to the population, it's to reduce it, which we've done. ... Our policy is not to send any new detainees to Guantanamo," she said.
Still, Rep. Peter King, R-New York, said Monday that it was "unfortunate that al Libi is on American soil, ending the interrogation process."
"It shows the inherent flaws in the U.S. policy decision to try (terror suspects) in the U.S. because once you arrive on U.S. soil, that ends the interrogation of these high value detainees," Kind said, said, adding would not have happened if al Libi had been sent to Guantanamo Bay and faced a military commission there.
King, a member of the House Homeland Security Committee and the House Permanent Select Committee on Intelligence, credited the government with giving advance notice of al Libi's arrival to New York Mayor Michael Bloomberg and NYPD Commissioner Ray Kelley, which allowed them to have security measures in place.
Journalist Ayman al-Kekli in Tripoli and CNN's Nic Robertson contributed to this story.