A key question in the early stages of the investigation had been how a trained terrorist could craft such a poorly made bomb, consisting of weak fireworks, propane tanks and nonexplosive fertilizer.

“He tried to lessen the explosive nature of the fertilizer that was used because he thought he would get a higher profile as he went to buy it,” Mr. Kelly told reporters, adding that Mr. Shahzad “sort of dumbed that down.”

Mr. Shahzad also used M-88 fireworks that were much weaker than other alternatives, Mr. Kelly said.

Law enforcement agencies, particularly the Federal Bureau of Investigation, maintain a number of “tripwires” designed to encourage people who sell everyday products that could be used to make explosives to notify agents of any suspicious behavior or purchases. Mr. Shahzad was apparently so worried about the tripwires that he deliberately built a weaker, less effective bomb.