'This is bigger than bin Laden': Petraeus says it's 'impossible to overstate' impact of Soleimani death

William Cummings | USA TODAY

Show Caption Hide Caption Are we really ready for a World War III? Fears are mounting around the world following the assassination of Iranian General Qasem Soleimani - but is World War 3 about to happen?

WASHINGTON – Retired Gen. David Petraeus said Sunday that the death of his former battlefield enemy, Iranian Gen. Qasem Soleimani, in a drone airstrike outside the Baghdad airport was a more dramatic event than the deaths of al-Qaida leader Osama bin Laden or Islamic State leader Abu Bakr al-Baghdadi.

Petraeus said during an interview on CBS News' "Face the Nation" that he considered Soleimani a "very capable" adversary during his time commanding troops in Iraq and that "it's impossible to overstate the significance of the attack" that killed Iran's top military figure.

Soleimani led Iran's elite Quds Force, an irregular group within the Islamic Revolutionary Guard Corps that supported militias loyal to Iran around the Middle East. Under Soleimani, the Revolutionary Guard trained Iraqi militants to fight U.S. troops after the 2003 invasion that toppled Saddam Hussein and taught them to make the roadside bombs that killed and maimed many American service members.

What you need to know: The death of Gen. Soleimani and the escalating situation with Iran

'I want to have peace': How Trump went from a vow to avoid conflict to an order to kill Iran general

The U.S. estimates that Iran was responsible for the deaths of about 600 American service members, which is about 17% of the total losses suffered in that conflict.

Petraeus said he was surprised to learn Soleimani had been killed.

"We'd never gone after him before, although I hasten to add that he never dared set foot inside Iraq to my recollection, when I was commanding the surge, nor in the time that I was the commander of U.S. Central Command," Petraeus said.

But he said Soleimani became bolder as Iran began to support Syrian leader Bashar al-Assad in that country's civil war and to bolster militias in Iraq to fight against ISIS.

"That was a period when he was helping Iraq go after the same enemy that we eventually helped Iraq defeat," Petraeus said of Soleimani's role in taking on ISIS. "And make no mistake about it, those militias and the Iraqi security forces could not have defeated the Islamic State in Iraq without our enabling forces, our drones, our precision munitions and our intelligence and advice."

Petraeus said he did not recall any discussions about taking out Soleimani when he was leading the U.S. forces in Iraq because "we just didn't have the opportunity." He said he could not discuss whether conversations along those lines took place during his time as director of the CIA.

The retired general said the biggest question following Soleimani's death is how Iran will respond.

"Will they dare to respond directly with Iranian missiles against our forces, our embassies, our bases, our shipping or what have you? Or do they continue to operate through proxies, which I'm pretty confident they will do," he said.

Petraeus said killing Soleimani was the equivalent of an enemy taking out a top U.S. general, the head of the CIA, the head of U.S. special forces and a Middle East presidential envoy all in one strike.

"This is bigger than bin Laden. It's bigger than Baghdadi," he said.

Whatever the Iranian response, Petraeus said it was critical that the U.S. finds a diplomatic way out of the escalating conflict. He called on the Trump administration to reach out to Iran "about how to get back to the nuclear deal that was had its strengths, as well as some shortcomings, to be sure."

Trump pulled the U.S. out of the deal, which was brokered by the Obama administration, that staved off Iran's development of nuclear weapons in exchange for sanctions relief. On Sunday, Iran effectively ended its commitment under the agreement.

Petraeus suggested the issue of Iran's support for Shiite militias in Iraq could be addressed in a new nuclear agreement.

"We truly do want to deescalate. Everyone is going to lose if this continues to ratchet upward," he said.