The portrait investigators have begun to piece together of the two brothers suspected of the Boston Marathon bombings suggests that they were motivated by extremist Islamic beliefs but were not acting with known terrorist groups — and that they may have learned to build bombs simply by logging onto the online English-language magazine of the affiliate of Al Qaeda in Yemen, law enforcement officials said Tuesday.

The investigation into the bombings is still in its earliest stages, and federal authorities were still in the process of corroborating some of the admissions that law enforcement officials said were made by the surviving suspect in the attacks,Dzhokhar Tsarnaev, 19. But they said some of his statements suggested that the two brothers could represent the kind of emerging threat that federal authorities have long feared: angry and alienated young men, apparently self-trained and unaffiliated with any particular terrorist group, able to use the Internet to learn their lethal craft.

Senator Marco Rubio, a Florida Republican who serves on the Senate Intelligence Committee, told reporters after emerging from a two-hour classified briefing with F.B.I. and intelligence officials Tuesday evening that the suspects were most likely radicalized over the Internet, but that investigators were still searching for possible sources of inspiration or support overseas.

“The increasing signals are that these were individuals who were radicalized, especially the older brother, over a period of time — radicalized by Islamist fundamentalist terrorists, basically using Internet sources to gain not just the types of philosophical beliefs that radicalized them, but also learning components of how to do these sorts of things,” Mr. Rubio told reporters.