Washington (CNN) It was an arresting headline in The Daily Beast on Monday: "Petraeus: Use Al Qaeda Fighters to Beat ISIS." The report didn't quote retired Gen. David Petraeus directly, but suggested he had told associates that he supports using "so-called moderate members of al Qaeda's Nusra Front to fight ISIS in Syria."

In an exclusive statement to CNN, Petraeus clearly feels that his view requires much more explanation, back story and nuance.

"We should under no circumstances try to use or coopt Nusra, an Al Qaeda affiliate in Syria, as an organization against ISIL," the retired general and former CIA director told CNN, using another name for ISIS. "But some individual fighters, and perhaps some elements, within Nusra today have undoubtedly joined for opportunistic rather than ideological reasons: they saw Nusra as a strong horse, and they haven't seen a credible alternative, as the moderate opposition has yet to be adequately resourced."

That said, Petraeus argued, "the question, therefore, is whether it might be possible at some point to peel off so-called 'reconcilables' who would be willing to renounce Nusra and align with the moderate opposition (supported by the U.S. and the coalition) to fight against Nusra, ISIL, and Assad. Doing so would require both the rise of much stronger, moderate opposition groups -- backed, again, by the U.S. and the coalition seeking to defeat ISIL -- and at the same time, intensified military pressure on all extremist groups."

As the architect of the 2006-2007 surge in Iraq, Petraeus clearly has informed opinions. A key to the surge was the U.S. decision to work with Sunnis and stabilize Iraq. That stability he helped create has been upset by ISIS, among other things.

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Of course, even if successful, the idea of the U.S. working with moderate members of al Qaeda's Nusra against ISIS would be controversial. But the fight against ISIS has already created strange bedfellows. The U.S. and Iran, for instance, disagree on most things, but they are both working against ISIS in the Middle East.

This context is key, Petraeus argues.

"In Iraq, during the Surge, Sunni tribes and insurgent groups that were previously aligned with AQI (al Qaeda in Iraq) switched sides because they concluded that there was a better alternative -- namely, partnership with us and, ultimately, the government of Iraq -- and because they saw that AQI was a losing bet," Petraeus told CNN. "Seeking to coopt those fighters was a very difficult decision for us because, in many cases, they had American blood on their hands."

"But, he continued, "it was in our national interest to do so, and the process of 'reconciliation' contributed significantly to the defeat of al Qaeda in Iraq in 2007-2008, a situation sustained for 2-3 more years. Sadly, of course, many of the agreements made during the Surge were subsequently broken, and that and other actions by the Iraqi government that alienated the Sunni Arab population in Iraq contributed to the resurrection of AQI in the form of ISIL."

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Petraeus was a well-regarded and highly decorated general, whose career at the CIA ended in controversy and scandal when he pled guilty to sharing classified information with his biographer and lover . But many in the foreign policy establishment still seek out his views, so his proposal will no doubt be taken seriously.

To summarize, Petraeus concluded that "although the situation in Syria today is different from that in Iraq during the Surge in numerous ways, we should nonetheless consider the possibility of trying to defeat radical groups in Syria not simply by killing or capturing the entirety of their membership -- though much of that will have to be done -- but also by splintering their ranks by offering a credible alternative to those 'reconcilable' elements of those organizations."