When a prominent Nigerian banker and former government official phoned the American Embassy in Abuja in October with a warning that his son had developed radical views, had disappeared and might have traveled to Yemen, embassy officials did not revoke the young man’s visa to enter the United States, which was good until June 2010.

Umar Farouk Abdulmutallab

The police searched the basement of a building in London, where it is believed that Umar Farouk Abdulmutallab had been a student.

Instead, officials said Sunday, they marked the file of the son, Umar Farouk Abdulmutallab, for a full investigation should he ever reapply for a visa. And when they passed the information on to Washington, Mr. Abdulmutallab’s name was added to...