Investigators believe that the views of the two brothers grew more radical over time, and were influenced at least partly by the Internet sermons of Mr. Awlaki. Separately, Dzhokhar Tsarnaev has told investigators that he and his brother learned to build the pressure-cooker bombs from reading Inspire, the onlinemagazine published by Al Qaeda in the Arabian Peninsula. 

The magazine’s first issue — which included an article titled “Make a Bomb in the Kitchen of Your Mom” — gave instructions about how to carry out crude, low-cost terrorist attacks. 

The man officials have identified as the creative force behind Inspire, an American citizen named Samir Khan, was killed in the same missile strike in Yemen that killed Mr. Awlaki. 

The new details of what Dzhokhar Tsarnaev has told authorities fill out a growing portrait of what the grievously wounded young man told investigators from his hospital bedside. 

In the course of questioning him about whether he knew of any other active plots or threats to public safety, Mr. Tsarnaev also admitted that he had been involved in laying the bombs that killed three people and injured more than 260 at the finish line of the marathon. He told investigators that he knew of no other plots and that he and his brother had acted alone, and he said he knew of no more bombs that had not been detonated. 

Since then, investigators have been seeking to verify Mr. Tsarnaev’s statements as part of the wide-ranging investigation into the lives of the two brothers, speaking with people who knew them and looking at everything from items they left behind in their homes and, in the case of Dzhokhar Tsarnaev, his dorm room, to the lengthy digital trail they left through their e-mails and posts on social media sites.
William K. Rashbaum and Serge F. Kovaleski contributed reporting from New York.