“He said, ‘Come in, sit down.’ He said, ‘Did you learn about what happened?’ ” Mr. Abu Ghaith testified at the trial. “He said, ‘We are the ones who did it.’ ”

The next day, at Bin Laden’s request, Mr. Abu Ghaith issued the first of a series of videotaped statements that helped Bin Laden spread his global message of terror, energize Qaeda fighters and recruit new ones, prosecutors told the jury.

Mr. Abu Ghaith has not been accused of having a role in the plot to attack the World Trade Center or of knowing about it. But when asked by a prosecutor if he “knew something big was coming from Al Qaeda,” he responded, “Yes.”

He was convicted on three counts: conspiracy to kill Americans, for which he could face life in prison; and providing material support to terrorists and conspiring to do so; each of those counts carries a maximum term of 15 years. The judge, Lewis A. Kaplan, said the defendant would be sentenced on Sept. 8.

Mr. Abu Ghaith, who used an Arabic interpreter in Federal District Court in Manhattan, appeared impassive as the judge’s deputy clerk, Andrew Mohan, read the verdict aloud, repeating “guilty” three times.

Mr. Abu Ghaith’s lead lawyer, Stanley L. Cohen, said later that his client was stoic and “at ease.”

“He has confidence that this is not the end but the beginning,” Mr. Cohen said, adding that there were “a number of compelling issues” for appeal.

Image Sulaiman Abu Ghaith had recorded impassioned speeches for Osama bin Laden after Sept. 11. Credit... Agence France-Presse — Getty Images

Crucial among them, Mr. Cohen said, was the judge’s refusal to allow the defense to introduce testimony from Khalid Shaikh Mohammed, the self-described architect of the Sept. 11 attacks who is detained at Guantánamo Bay. Mr. Cohen had argued that Mr. Mohammed, with his unsurpassed knowledge of Qaeda operations, could help exculpate his client.