CNN  — 

The biggest threat to Iraq’s long-term stability isn’t ISIS, according to Gen. David Petraeus, who led the U.S. surge during the Iraq War.

Instead, Petraeus said the Iran-backed Shiite militias who are helping to fend off ISIS are “the foremost threat” to long-term stability in Iraq, according to an interview with the Washington Post. The comments provide the most expansive glimpse yet into how Petraeus may be helping to shape the Obama administration’s strategy in Iraq as he continues to advise the National Security Council on the issue.

Those militias, many funded and trained by Iran, have been an important part of efforts to push ISIS out of Syria, but they have also been accused of war crimes – allegedly murdering not just ISIS fighters, but also Sunni civilians.

“They have, to a degree, been both part of Iraq’s salvation but also the most serious threat to the all-important effort of once again getting the Sunni Arab population in Iraq to feel that it has a stake in the success of Iraq rather than a stake in its failure,” Petraeus told the Post. “Longer term, Iranian-backed Shia militia could emerge as the preeminent power in the country, one that is outside the control of the government and instead answerable to Tehran.”

Petraeus’ comments come as the U.S.’s strategy to defeat ISIS is facing increased scrutiny on Capitol Hill as lawmakers debate how to enshrine the U.S.’s war against ISIS into legislation formally authorizing military force.

Lawmakers pressed the U.S.’s top national security officials during a hearing last week on the growing influence of Iran in the region and the long-term implications for security – something Defense Secretary Ash Carter and Joint Chiefs Chairman Gen. Marin Dempsey said raised legitimate concerns.

“We are all concerned about what happens after the drums stop beating and ISIL is defeated,” Dempsey said.

Iran’s growing influence in the region dates back to the U.S. invasion of Iraq, which toppled Saddam Hussein’s Sunni regime and put Shiite Muslims – the country’s dominant group – in power. Iran, also a Shiite-majority country, seized the opportunity to rekindle ties with its formerly rival neighbor.

And the ISIS threat also gave Iran an opening to expand its influence in the region, sending its elite Revolutionary Guards to Iraq to train, advise and fight ISIS, whose advances into Iraq sounded alarm bells in Iran.

Despite ongoing negotiations with the U.S., Iran, which supports destabilizing terror groups in the region, remains a threat to U.S. allies and the U.S.’s strategic interests – like Iran’s support of the Assad regime in Syria.

The situation in Syria is also one Petraeus said he is “profoundly worried about.”

“Until it is capped, it is going to continue to spew radioactive instability and extremist ideology over the entire region,” said Petraeus, who also served as President Barack Obama’s CIA director. “Any strategy to stabilize the region thus needs to take into account the challenges in both Iraq and Syria. It is not sufficient to say that we’ll figure them out later.”

The Obama administration’s strategy in dealing with the still-ongoing civil war in Syria has been just one of the many magnets for criticism from GOP lawmakers, the most prominent of which is Sen. John McCain, who has argued the U.S. should do more to stem the violence in that country – notably, arming moderate rebels fighting the Syrian regime.

The Obama administration has trained and armed some opposition forces and is still trying to identify the ideal partners for the U.S. on the ground in Syria, but those efforts would only be aimed at defeating ISIS, not the Assad regime.

And the U.S. has focused on fighting ISIS, leading a coalition that is pummeling the extremist group from the air while coordinating with local forces on the ground. Those efforts have spared the Syrian regime.