A federal investigation of how David H. Petraeus’s biographer obtained numerous classified records is focusing on whether the retired general’s staff gave her sensitive documents at his instruction, according to federal officials familiar with the inquiry.

Petraeus aides and other high-ranking military officials were often tasked by Petraeus and other top commanders to provide military records and other documents to Paula Broadwell for her work as Petraeus’s biographer, former staff members and other officials told The Washington Post.

Broadwell, a married Army reservist, frequently visited Petraeus in Afghanistan when he was in charge of the war there. She repeatedly sought records that she said Petraeus wanted her to have, according to the former staff members and officials, who spoke on the condition of anonymity because the inquiry is ongoing.

The focus on the role of military staff members adds a new chapter to the complicated ethics scandal that led Petraeus to abruptly resign as CIA director on Nov. 9. His affair with Broadwell also has put the personal communication of Marine Gen. John R. Allen, Petraeus’s successor as commander of the Afghan war, under scrutiny by the Pentagon.

Petraeus and Broadwell have told FBI investigators that Petraeus did not provide her with classified information, law enforcement officials said. Attorneys for the two declined to respond to specific questions for this article, as did Broadwell’s spokeswoman, Dee Dee Myers of the Glover Park Group. FBI officials also declined to comment.

The investigation of the origins of classified material in Broadwell’s possession began in the summer as part of a routine FBI inquiry into harassing e-mails sent to a woman in Tampa. The messages warned the woman, socialite Jill Kelley, to stay away from Petraeus and were traced to anonymous accounts set up by Broadwell, according to law enforcement officials involved in the case.

The investigation uncovered e-mails between Petraeus and Broadwell that exposed their affair and led to his resignation. The inquiry also turned up questionable e-mails between Kelley and Allen, who, like Petraeus, had met the Tampa woman while serving at U.S. Central Command, known as Centcom.

The initial investigation focused on whether Broadwell’s harassment of Kelley constituted a crime. But the early e-mails showed that the sender had access to detailed schedules for Petraeus and Allen, which raised concern about possible national security violations.

Broadwell turned over her computer to the FBI in late summer, and agents discovered that it contained low-level classified material. On Nov. 12, the FBI searched her home in Charlotte and carried away additional evidence that she had classified documents, law enforcement officials said.

The documents have been described as sensitive but relatively benign. Officials who have been briefed on them said they were mostly schedules and PowerPoint presentations classified as “secret.”

In piecing together how Broadwell came to possess the material, FBI investigators have sought to determine whether it was provided by aides to Petraeus when he was head of Centcom in Tampa from 2008 to June 2010 or when he was commander of U.S. and international forces in Afghanistan from July 2010 to July 2011. He resigned from the Army to become CIA director in September 2011.

Some former Petraeus staff members said in interviews that they were annoyed by and concerned about Broadwell’s requests for information, which sometimes involved sensitive material. At the time, she was working on her book about Petraeus, which was published in January. She also maintained a “top secret” security clearance as an officer in the Army reserves.

One former Defense Department official said that when staff members at the International Security Assistance Force headquarters in Kabul questioned Broadwell’s access to certain classified records, she assured them that Petraeus had approved her seeing the material.

“Even if he did not directly give her classified information, he was allowing his name to be used,” said the former official, who spoke on the condition of anonymity to discuss the matter freely. “I would be surprised if anyone would raise a question for anything below ‘top secret.’ ”

Those close to Petraeus’s inner circle said Broadwell could have easily collected classified briefing materials distributed during meetings that were not supposed to leave the secure facilities where such conferences take place. Because of her unusual status, she probably would not have been subject to a search when leaving military offices, they said.

A former Petraeus associate said Broadwell could have obtained electronic copies of classified material from a little-known internal military research arm that had carte blanche to review and consolidate classified material. The research arm, which was part of Centcom, had a special ability to make electronic copies of sensitive material and transfer it to computer disks. A spokesman at Centcom in Tampa declined to comment.

Copying and e-mailing classified material is prohibited except on secure networks. A former colleague of Broadwell’s told The Post last week that he received a disk from Broadwell that contained documents marked “secret,” including schedules for Petraeus and other high-ranking officers and military PowerPoints.

The level of sensitivity of the records Broadwell obtained is unclear. President Obama said at a news conference last week that he had seen no evidence that the release of these records “in any way would have had a negative impact on our national security.”

But even low-level classified records typically cannot be kept on someone’s personal computer or in their home.

“Using Centcom as an example, I can count on one hand the number of people who have clearance to have classified material at their home,” one former Petraeus associate said. “General Petraeus was one.”

On Nov. 12, FBI agents searched Broadwell’s Charlotte home while she was with her family in Washington. They removed dozens of boxes of records as well as computer disks and multiple central processing units, which store the deeper memories of desktop computers. Broadwell has been cooperating with the investigation.

Two days after the FBI search at her home, the Army suspended Broadwell’s security clearance.

Kimberly Kindy contributed to this report.