The White House immediately rejected the idea of an amnesty, but Attorney General Eric H. Holder Jr. said recently that he would be open to talking about some kind of deal for Mr. Snowden if he returned from Russia.

Image Vice Adm. Michael S. Rogers in 2012. Credit... Nathan L. Guimont/Agence France-Presse — Getty Images

If confirmed, Admiral Rogers will succeed Gen. Keith B. Alexander, who has served as N.S.A. director for nearly nine years and was the first to direct both the civilian spy agency and the Cyber Command. He announced last year that he would retire in March. Since then Admiral Rogers has been considered the most likely successor, because of his experience in code-breaking — the reason the N.S.A. was created by President Harry S. Truman six decades ago — and his understanding of the design of America’s new arsenal of cyberweapons.

Mr. Obama interviewed the admiral for the job last week, though the president left it to Defense Secretary Chuck Hagel, traveling in Poland on Thursday, to announce the appointment. Mr. Hagel pointed to the challenges the new director will face in a statement, saying, “Vice Admiral Rogers would bring extraordinary and unique qualifications to this position as the agency continues its vital mission and implements President Obama’s reforms.”

He added, “I am also confident that Admiral Rogers has the wisdom to help balance the demands of security, privacy and liberty in our digital age.”

A statement issued minutes later by the director of national intelligence, James R. Clapper Jr., made no reference to proposed policy changes at the N.S.A. or the need to conduct the kind of balancing Mr. Hagel referred to — a reflection, perhaps, of the arguments Mr. Clapper has made internally that many of the proposals undercut the N.S.A.’s ability to protect the country.

Admiral Rogers’s appointment would clearly be welcomed in the military intelligence community, where he is regarded as a trusted insider. He began his career not in intelligence or electronics, but in traditional surface warfare. He was commissioned via the Naval Reserve Officer Training Corps after graduating from Auburn in 1981, and worked in combat naval gunfire support, serving in operations off Grenada, Beirut and El Salvador.

But in 1986, after five years in the service, he made a leap that prepared him for the post he is now likely to take up: He began specializing in cryptology, and trained in both electronic and information warfare. A number of assignments to various warships and carrier strike groups followed, taking him to United States and NATO missions in the Balkans and in Afghanistan.