In papers in Manhattan federal court, prosecutors asked US District Judge Lewis A Kaplan to permit the "critically important evidence" against Abu Anas al-Libi.
Al-Libi was nabbed in Tripoli in October 2013 and brought to the United States to face trial in the 1998 bombings of US embassies in Africa that killed 224 people. He has pleaded not guilty in the attacks, which killed a dozen Americans.
Al-Libi's lawyer did not immediately return a message seeking comment.
Prosecutors said the letters, including two written by al-Libi, prove he actively participated in al-Qaida after spending eight years incarcerated in Iran. They said the letters would provide jurors in the trial scheduled to begin Jan. 12 with "powerful, direct, proof of al-Qaida's conspiracies to bomb and kill Americans, as well as Anas al-Libi's knowing and intentional participation in them."
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In one 2010 letter to bin Laden, al-Libi asks "God to reunite me with you soon under the banner of Islam and the Islamic state and the banner of jihad," the government said.
The government also wants to show jurors four letters to bin Laden from his chief deputy discussing al-Libi's continued participation in al-Qaida, prosecutors said.
In an October 13, 2010, letter written by al-Libi, he responds to a bin Laden request that he describe his flight from Afghanistan to Iran in late 2001 or early 2002 and his release from Iranian detention and his return to Pakistan in 2010, prosecutors said.