WASHINGTON — The man with the wire-rim glasses and bushy beard, speaking calmly in American-accented English, is familiar from dozens of Web videos urging violent jihad against the United States.

But in one astonishing clip, recorded more than a year before the man, Anwar al-Awlaki, was killed by a C.I.A. drone strike in Yemen, the American-born cleric had a very different mission: to propose marriage to a third wife.

“This message is specifically for Sister Aminah,” Mr. Awlaki says in the video to his future bride, a comely 32-year-old blonde from Croatia who he hoped would join him in his fugitive existence. The woman had expressed fervent admiration for Mr. Awlaki on his Facebook page and later made clear in her own video reply that she shared his radical views, saying, “I am ready for dangerous things.”

Neither Mr. Awlaki nor his prospective wife knew it, but their match was being managed by a Danish double agent as part of an attempt to help the Danish intelligence service and the C.I.A. find the cleric’s hiding place in Yemen. The attempt failed, but the undercover agent, Morten Storm, 36, a former motorcycle gang member who had converted to Islam, continued to communicate with Mr. Awlaki. When Mr. Awlaki was killed in a drone strike on Sept. 30, 2011, Mr. Storm was certain his efforts had been instrumental in it.