Former CIA chief General David Petraeus said sorry Tuesday for the "mistake" which triggered his resignation last year, in his first public speech since quitting due to an extra-marital affair.

Addressing a military audience in Los Angeles, Petraeus voiced regret for the "pain" caused by his relationship with his biographer Paula Broadwell, pledging to try to "make amends to those I have hurt and let down."

"I join you keenly aware that I am regarded in a different light now than I was a year ago," Petraeus told over 600 veterans and Reserve Officers' Training Corps students, hosted by the University of Southern California (USC) in a Los Angeles hotel.

"I am also keenly aware that the reason for my recent journey was my own doing," said the former head of the Central Intelligence Agency (CIA) and before that top US general, who spearheaded the "surge" in Iraq.

"So please allow me to begin my remarks this evening by reiterating how deeply I regret -- and apologize for -- the circumstances that led me to my resignation from the CIA and caused such pain for my family, friends and supporters."

Petraeus, America's most celebrated military leader in a generation, stepped down on November 9 as head of the CIA after admitting to an affair with Broadwell, a counter-terrorism expert and lieutenant-colonel.

The FBI stumbled upon the affair when Jill Kelley, a Florida socialite and friend of the Petraeus family, asked investigators to look into threatening emails that turned out to be from an apparently jealous Broadwell.

Towards the end of his 25-minute address Petraeus said: "I know that I can never fully assuage the pain that I inflicted on those closest to me and on a number of others.

"I can, however, try to move forward in a manner that is consistent to the values to which I subscribed before slipping my moorings and, as best as possible, to make amends to those I have hurt and let down.

"Life doesn't stop with such a mistake; it can and must go on," added the former CIA head, who was given a standing ovation at the start and end of his address.