The fact that investigators discovered suspicious files suggests that the breach involved the installation of malicious software, or malware, said Ed Stroz, a former FBI agent who is co-president of Stroz Friedberg, a firm that investigates cyberattacks.

In attacks on companies, Mr. Stroz said, hackers often plant malware that acts as a back door, which allows them to deliver other malicious programs to do other tasks, which could include copying sensitive data and delivering it to the intruder.

Malware could have been installed any number of ways, including with an attack through the Web interface of Directors Desk or by infiltrating an executive’s computer by tricking him into opening an attachment or clicking on a link to a malicious Web page in an e-mail.

Nasdaq now handles about 19 percent of stock trading in the United States, compared with 27 percent by the larger New York Stock Exchange and its electronic trading arm.

In a statement, the New York Stock Exchange said: “We take any potential threat seriously and we continue working at the highest levels of security and integrity.” The N.Y.S.E. would not say whether there had been any attempts to breach its systems or whether it had been contacted by federal investigators.

News of the breach was originally reported in The Wall Street Journal.

Nasdaq said it had refrained from notifying its customers of the breach at the request of the Justice Department, “in order to facilitate the continuing investigation,” but that when the Journal article appeared it consulted with authorities and decided to send out notice.

The Journal article said the investigation showed some evidence pointing toward Russia. One government official said investigators were specifically looking into that possibility, although the official said, “I don’t know what the basis for the belief is.”