The N.S.A. is not just intercepting the communications of Americans who are in direct contact with foreigners targeted overseas, a practice that government officials have openly acknowledged. It is also casting a far wider net for people who cite information linked to those foreigners, like a little used e-mail address, according to a senior intelligence official.

While it has long been known that the agency conducts extensive computer searches of data it vacuums up overseas, that it is systematically searching — without warrants — through the contents of Americans’ communications that cross the border reveals more about the scale of its secret operations…

Government officials say the cross-border surveillance was authorized by a 2008 law, the FISA Amendments Act, in which Congress approved eavesdropping on domestic soil without warrants as long as the “target” was a noncitizen abroad. Voice communications are not included in that surveillance, the senior official said.