A U.S. official familiar with the e-mails Allen sent to Kelley described them as warranting the investigation.
"If they got out, John Allen would be very embarrassed by them," said the official, who added that there was no evidence of physical contact between the two.
The official said that the e-mails under investigation are from Allen.
But a senior official close to Allen told CNN on Tuesday that the e-mails contained nothing pointing to sex or anything of a romantic nature. Allen may have said, informally, "thanks sweetheart" in an e-mail, the official close to Allen said.
"Anyone who knows him knows his style; he has a habit of replying to every single e-mail (he is sent). Kelley would e-mail his business and personal accounts," the official said.
It will be up to the Defense Department's inspector general to decide if the e-mails' content represents conduct unbecoming an officer, said a third source, a senior U.S. official.
Allen has yet to be questioned by Defense Department inspector general staff, but that could be completed in days, a U.S. official with knowledge of the investigation said.
Allen, who was once stationed at the base, has denied wrongdoing, a senior defense official said. In a statement, Col. John Baker, the chief defense counsel of the Marine Corps, said Allen "fully intends to cooperate" with the inspector general's investigators.
Broadwell's anonymous e-mail to Allen was sent after May, perhaps in June, the official said.
The e-mail, which had also been sent to a number of other officers, bore the handle "kelleypatrol -- or something similar," the official said.
He described the e-mail as "a warning that Kelley was a seductress or something along those lines" and said it was vaguely threatening, but above all weird.
"Allen did not know it was (from) Broadwell," the official said.
The official also said it was unclear when Kelley went to the FBI or whether Allen's warning to her was the trigger, but that Allen saw nothing in the e-mail's wording to warrant referral by him to the FBI.
Kelley's version differs from one offered by the senior official close to Allen, who said it was Allen who received an anonymous e-mail about Kelley, and tipped her off that someone was threatening her.
One of the sources familiar with Kelley said she first mentioned the alleged harassment in a casual conversation with an FBI agent whom she knew socially. She did not seek him out for action on the matter, but he was happy to help, the source said. The source added that Kelley did not know at first that the e-mails led to Petraeus.
A source familiar with Kelley's version of events said the anonymous e-mails traced to Broadwell began in June. It wasn't until two months later that the FBI told Kelley who had sent the e-mails, said the source, adding that Kelley does not know Broadwell.
The general counsel for the Federal Law Enforcement Officers Association identified Frederick Humphries as the agent initially contacted by Kelley about the anonymous e-mails.
The counsel, Lawrence Berger, said Humphries and his wife had been friends for years with Kelley and her husband.
Berger said Humphries took Kelley's concerns over the e-mails to the "appropriate components" at the FBI to investigate. "He reported it to the proper channels and had no further part on the case."
Kelley, 37, and her husband have released a statement saying they have been friends with Petraeus and his family for more than five years and asked for privacy.
A source close to Kelley said Wednesday that Kelley said she had not had a sexual relationship with Petraeus or Allen.
In mid-May, Allen got the first anonymous e-mail from someone using the handle "Kelleypatrol" that maligned Kelley and warned him to be wary of her, the source said.
Allen forwarded it to Kelley, thinking she might have sent it as a joke, but she told him she had not, the source continued.
The move to delay Allen's nomination was "a prudent measure until we can determine what the facts are, and we will," Panetta told reporters Wednesday. "No one should leap to any conclusions."
He said Allen "certainly has my continued confidence to lead our forces," a view shared by Obama, White House spokesman Jay Carney said.