Petraeus - the most celebrated US general of his generation, who was credited with turning around the war in Iraq - resigned last week to pre-empt revelations of an affair with his biographer Paula Broadwell, a married army reservist.
A lawyer acting for the US commander in Afghanistan, General John Allen, who is also under investigation over e-mails he sent to a Florida socialite, said his client would fully cooperate with the Pentagon probe.
Petraeus and Allen were exposed after Jill Kelley, a 37-year-old Tampa hostess who organized parties for military officers, complained to an FBI agent friend of threatening e-mails, which turned out to be from Broadwell.
The scandal has rocked the Washington security establishment but, beyond any personal failings it may have revealed, Obama said he had seen no evidence it had harmed the security of the nation or its troops.
"I have no evidence at this point from what I have seen that classified information was disclosed that in any way would have a negative impact on our national security," he said at his first news conference since his re-election.
"General Petraeus had an extraordinary career," he said. "But by his own assessment, he did not meet the standards that he felt were necessary as the director of the CIA with respect to this personal matter."
Petraeus is due to testify behind closed doors to Congress on Friday about the Sept 11 assault in Benghazi, Libya, which killed four US citizens, including US ambassador Chris Stevens and two former Navy SEALs working for the CIA.
The FBI launched the investigation after Kelley alerted them to the threatening e-mails, which indicated the sender had detailed knowledge of the travel schedules of both Petraeus and Allen, the Washington Post reported.
The Post cited defense officials as saying that authorities at MacDill Air Force Base in Tampa had revoked Kelley's entry badge, which granted her the same access as relatives of military personnel and retirees.
The White House expressed confidence in Allen, after the married four-star general was placed under investigation by FBI agents. Allen denies any sexual liaison with Kelley, but some e-mails, reportedly "flirtatious" in nature, could be a breach of military rules.
Agence France-Presse in Washington