"How did you get the information, what's the basis for the investigation, who did you talk to, were you working with prosecutors, all those issues have to be looked at," including why the intelligence committees weren't told of the investigation until just before Petraeus' resignation, he said.
Petraeus will testify Friday before the House Intelligence Committee about Libya, panel spokeswoman Susan Phalen said.
Lawmakers are also concerned over reports that Broadwell had classified information on her laptop, though FBI investigators say they concluded there was no security breach.
FBI agents who contacted Petraeus told him that sensitive, possibly classified documents related to Afghanistan were found on her computer, the general's associates said. He assured investigators they did not come from him, and he mused to his associates that they were probably given to her on her reporting trips to Afghanistan by commanders she visited in the field there.
One associate also said Petraeus believes the documents described past operations and had already been declassified, although they might have still been marked "secret."
Feinstein, asked by reporters if there was a national security breach with the Petraeus affair, said she had "no evidence that there was at this time."
Feinstein said that Petraeus himself would testify before Congress — but not about the affair. She said he had agreed to appear to talk about the Libya attack on Sept. 11 that killed the U.S. ambassador and three other Americans, but she said no date had been set.
Allen has been allowed to stay in his job as commander of the Afghan war, providing a leading voice in White House discussions on how many troops will remain in Afghanistan — and for what purposes — after the U.S.-led combat operation ends in 2014.
But Obama has put on hold Allen's nomination to become the next commander of U.S. European Command as well as the NATO supreme allied commander in Europe until Pentagon investigators are able to sift through the 20,000-plus pages of documents and emails that involve Allen and Kelley.
Defense Secretary Leon Panetta, at a news conference in Perth, Australia, said, "No one should leap to any conclusions" about Allen, and said he is fully confident in Allen's ability to continue to lead in Afghanistan. He added that putting a hold on Allen's European Command nomination was the "prudent" thing to do.
Associated Press writers Kimberly Dozier, Pauline Jelinek, Lolita Baldor, Michael J. Sniffen, Eileen Sullivan and Adam Goldman in Washington and Dale Wetzel in Bismarck, N.D., contributed to this report.
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