* Developments could quash hopes for early end to case
* Obama sees "no evidence" of security breach in Petraeus, Allen cases
* Allen pledges to "fully cooperate" in probe
WASHINGTON, Nov 14 (Reuters) - A computer used by Paula Broadwell, the woman whose affair with CIA Director David Petraeus led to his resignation, contained substantial classified information that should have been stored under more secure conditions, law enforcement and national security officials said on Wednesday.
The contents and amount of the classified material - and questions about how Broadwell got it - are significant enough to warrant a continuing investigation, the officials said. They spoke on condition of anonymity because they are not authorized to comment publicly.
The details about material held by Broadwell, a reserve officer in military intelligence, emerged Wednesday as the Pentagon suspended Broadwell's security clearance.
Late Wednesday, the House intelligence committee announced Petraeus would testify on Friday behind closed doors about t he attack on the U.S. Co n sulate in Benghazi, Libya. L e aders of the House and Senate intelligence committees were briefed Wed nesday on the Petraeus matter by leaders of the FBI and CIA.
There is growing concern among military and law enforcement officials about the potential fallout from the affair between Petraeus and Broadwell, who co-authored a biography of the retired general.
During a news conference at the White House on Wednesday, President Barack Obama said there was no indication so far that any classified information had been disclosed as a result of the affair.
Obama also said that for now, he would refrain from judging whether he should have been told earlier than last Wednesday about the probe involving his CIA chief, who resigned on Friday before the affair became public.
"I am withholding judgment with respect to how the entire process surrounding General Petraeus came up. We don't have all the information yet," Obama told a White House news conference.
The president noted that had he known earlier, he might have been open to accusations of interference in a politically sensitive law enforcement matter.
Broadwell's security clearances gave her access to certain classified material, several officials said. Government rules require such material to be stored in secure locations or computers.
Two officials familiar with the case said investigators are asking whether Broadwell followed government rules for handling classified information.
FBI investigators searched Broadwell's residence in Charlotte, North Carolina, late Monday, an action that officials said occurred with Broadwell's consent.
Attempts to reach Broadwell, who has remained mainly out of the public eye, have been unsuccessful. She was seen late Tuesday at her brother's home in Washington, D.C.
During the FBI investigation that led to the discovery of the affair between Petraeus and Broadwell, both individuals denied that Petraeus had supplied her with any classified information and the FBI accepted those explanations, law enforcement sources have said.
CRIMINAL CHARGES UNLIKELY
Law enforcement officials also have said that they believe the continuing FBI probe into the matter is likely to end without criminal charges. If Broadwell is found to have mishandled classified information, she could face action under administrative security regulations.
Still, the latest developments could quash hopes among some at the Justice Department and in Congress for a quick end to a scandal that this week also ensnared the commander of U.S. and NATO forces in Afghanistan, Marine General John Allen.
In a statement late Wednesday issued by the Marine Corps' chief defense counsel, Allen pledged to resolve the questions surrounding his email communications with Tampa socialite Jill Kelley, who is also at the center of the Petraeus case.
The retired four-star Army general has made no public statement since he announced his resignation as CIA chief on Friday.
Petraeus has agreed, however, to testify before Congress about the attack on the U.S. Consulate in Libya, that killed four Americans, amid questions over the CIA's actions before, during and after the assault on Sept. 11, 2012.
C.A. "Dutch" Ruppersberger, ranking Democratic member of the House intelligence committee, said Congress still wanted to hear from Petraeus on the Benghazi attack.
"When a situation like this occurs with Gen. Petraeus, we have to make sure that the CIA is moving forward on their mission and that in no way will this affect their ability to do their work," Ruppersberger said.
There is no protocol in federal law that would have required senior officials - like FBI Director Robert Mueller or Attorney General Eric Holder - to inform the president about the Petraeus investigation sooner, a former Justice Department official said.
The most recent written guidance was issued in 2007 by Michael Mukasey, then the attorney general. The Justice Department should advise the White House about a criminal matter "only where it is important for the performance of the president's duties and where appropriate from a law enforcement perspective," the memo reads. It leaves interpretation of those terms to the attorney general and the deputy attorney general.
"It's the quintessential judgment call for an attorney general to decide whether to share this information and when to share it with the White House," the former official said. "But this was Attorney General Holder's call to make."
ALLEN PLEDGES COOPERATION
This week, U.S. Defense Secretary Leon Panetta asked the Pentagon's inspector general to examine potentially inappropriate communications between Allen and Kelley, and recommended that Obama halt Allen's nomination to command US and NATO forces in Europe, which he did.
Defense officials have said Allen did not have a romantic relationship with Kelley, a 37-year-old wife and mother who is described as a prominent presence in military circles in Tampa.
She may have been seen as a rival by Broadwell, who sent Kelley a series of anonymous, harassing emails that touched off an investigation that uncovered evidence of an affair between Petraeus and Broadwell, according to a law enforcement source.
Allen and Kelley communicated often enough over the past two years to produce between 20,000 and 30,000 pages of email and other messages, which were turned over to Defense Department investigators on Sunday.
"To the extent there are questions about certain communications by General Allen, he shares in the desire to resolve those questions as completely and quickly as possible," the Marines' chief defense counsel, Colonel John G. Baker, said in a statement.
Allen remains in his post as commander in Afghanistan.
A senior defense official told Reuters the messages with Kelley were seen as inappropriate because they were "flirtatious" in nature, not because they dealt with sensitive information.
But another U.S. official said the Pentagon only decided to refer the matter for investigation after an initial look found the communications to be of "a sufficient character" to warrant further review.