He told the sheik that the charges against him, ordering the terror conspiracy, are fundamentally different from the charges against all the other defendants, who are accused of plotting to carry out the orders.
He said it would be much easier to show that a person had information than it would be to show that there was reason to believe the person was involved in the terror conspiracy.
Mr. Nosair is accused of having murdered Rabbi Meier Kahane in 1991, a crime that the Government says was part of the overall terror conspiracy.
On Sunday a Federal jury convicted Sheik Omar Abdel Rahman and nine followers on 48 out of 50 charges relating to that terror conspiracy.
Then came the 1995 trial of Sheik Omar Abdel Rahman, accused in a terror conspiracy that included the Trade Center bombing.
Both received life sentences without parole for a terror conspiracy, in Nosair's case life plus 15 years imprisonment.
Part of Ms. Doi's call was played earlier this year at the trial of Zacarias Moussaoui, who was accused of participating in the terror conspiracy.
LaRose was the only American woman in recent years to have been charged in the U.S. with terrorist violations and attempting to foment a terror conspiracy to kill someone overseas.
Also charged with terror conspiracy are Rafiq Sabir, a doctor from Florida, and Mahmud Faruq Brent, a paramedic from Washington, D.C.
With yesterday's testimony, the prosecution seemed intent on portraying Mr. Ajaj as a Muslim militant engaged in Islamic combat across the globe, the kind of man who might engage in a terror conspiracy in the United States.