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The Pentagon inspector general wrote to General Allen that the investigation had found no improprieties in the e-mail communications with the socialite, Jill Kelley, officials said.

The communications were discovered during an F.B.I. investigation into anonymous e-mails to Ms. Kelley warning her to stay away from David H. Petraeus, then the C.I.A. director. The F.B.I. found that the e-mails had been sent by Paula Broadwell, Mr. Petraeus's biographer; he admitted to having had an affair with Ms. Broadwell and resigned his position on Nov. 9.

Like General Allen, Mr. Petraeus, a retired four-star general, was a social acquaintance of Ms. Kelley's when he was stationed at MacDill Air Force Base in Tampa, headquarters of Central Command.

Even before Tuesday's disclosure, the outcome of the inspector general's inquiry was not unexpected. The decision was first reported on the Web site of The Washington Post.

What remains unknown is the fate of General Allen's nomination to become the top NATO commander, as was planned before the disclosure of the e-mails. General Allen could be nominated to that position or another senior post, or he could retire.

"The final decision has not yet been made on General Allen's nomination," one senior official said.

During the inquiry, about 15 investigators on the Pentagon inspector general's staff focused on 60 to 70 e-mails that "bear a fair amount of scrutiny," according to an official who was briefed on the inquiry.

Pentagon officials described the voluminous correspondence between General Allen and Ms. Kelley as potentially "inappropriate communication." Law enforcement officials say the e-mails number in the hundreds and cover two and a half years starting in 2010, when General Allen was the deputy commander of Central Command.

The F.B.I. sent the e-mails between General Allen and Ms. Kelley to the Pentagon on Nov. 11.

Investigators had been trying to determine whether the e-mails violated Defense Department policy, government regulations or military law. At issue was whether the e-mails contained inappropriate language on a government computer, whether they indicated an inappropriate relationship as defined under military law, whether they involved more than an incidental use of government property for personal matters and whether there were security breaches.

Gen. Joseph F. Dunford Jr. has been confirmed to succeed General Allen as part of a standard rotation, and is expected to take up command in Kabul in the coming weeks.